How do we know what day of the week Jesus died?

Is there any way to reconcile these accounts?

It's not obvious what needs to be reconciled.

For instance, consider "the Bible mentions many times that Jesus would rise on the third day. If Wednesday was the first day of Jesus's death, then Friday would be the third day":

Jesus was buried just before sunset on Wednesday.
Given that a new day begins at sunset, I don't think any reasonable person would count the few minutes preceding sunset as a different day; they would consider him to have been buried just as a new day begins.
So the first day ran from Wednesday sunset to Thursday sunset.
The second day ran from Thursday sunset to Friday sunset.
The third day ran from Friday sunset to Saturday sunset.

If Jesus arose just before sunset on Saturday, that would be 72 hours, exactly 3 days and 3 nights after he was buried.
The only point one could argue here is whether the few minutes before sunset must be counted as a fourth day.

If you think this seems a little contrived or forced, compare it with the traditional explanation that somehow crams three days and three nights into less than 36 hours, and at the same time somehow manages to have the women preparing spices before the sabbath and then buying them after the sabbath.

I'm not claiming the proof of this timeline is irrefutable, but it certainly is far simpler and much more convincing than the alternatives, which are mostly based on tradition rather than on scripture.
Occam's Razor would suggest that a resurrection late on Saturday would be the explanation that is least in need of reconcilliation.

How do we know what day of the week Jesus died?

The Scriptures do not explicitly tell us what day of the week Jesus was crucified. Traditionally as well as popular belief is that it happened on a Friday. However a few hold that it may thane been on a Wednesday or even a Thursday.

We have to equally keep in mind what the word day means according to Jewish understanding at the time of the Apostles.

The day is reckoned from evening to evening—i.e., night and day—except in reference to sacrifices, where daytime and the night following constitute one day (Lev. vii. 15) - Day (Jewish Encyclopaedia)

The Catholic Encyclopedia states that Friday was the day the Early Church commemorated the death of Christ and this is known in English speaking countries as Good Friday.

Definition and etymology

Good Friday, called Feria VI in Parasceve in the Roman Missal, he hagia kai megale paraskeue (the Holy and Great Friday) in the Greek Liturgy, Holy Friday in Romance Languages, Charfreitag (Sorrowful Friday) in German, is the English designation of Friday in Holy Week — that is, the Friday on which the Church keeps the anniversary of the Crucifixion of Jesus Christ.

Parasceve, the Latin equivalent of paraskeue, preparation (i.e. the preparation that was made on the sixth day for the Sabbath; see Mark 15:42), came by metonymy to signify the day on which the preparation was made; but while the Greeks retained this use of the word as applied to every Friday, the Latins confined its application to one Friday. Irenaeus and Tertullian speak of Good Friday as the day of the Pasch; but later writers distinguish between the Pascha staurosimon (the passage to death), and the Pascha anastasimon (the passage to life, i.e. the Resurrection). At present the word Pasch is used exclusively in the latter sense. The two Paschs are the oldest feasts in the calendar.

From the earliest times the Christians kept every Friday as a feast day; and the obvious reasons for those usages explain why Easter is the Sunday par excellence, and why the Friday which marks the anniversary of Christ's death came to be called the Great or the Holy or the Good Friday. The origin of the term Good is not clear. Some say it is from "God's Friday" (Gottes Freitag); others maintain that it is from the German Gute Freitag, and not specially English. Sometimes, too, the day was called Long Friday by the Anglo-Saxons; so today in Denmark.

The following article may be of interest to some.

The Bible does not explicitly state on which day of the week Jesus was crucified. The two most widely held views are Friday and Wednesday. Some, however, using a synthesis of both the Friday and Wednesday arguments, argue for Thursday as the day.

Jesus said in Matthew 12:40, “For as Jonah was three days and three nights in the belly of a huge fish, so the Son of Man will be three days and three nights in the heart of the earth.” Those who argue for a Friday crucifixion say that there is still a valid way in which He could have been considered in the grave for three days. In the Jewish mind of the first century, a part of day was considered as a full day. Since Jesus was in the grave for part of Friday, all of Saturday, and part of Sunday—He could be considered to have been in the grave for three days. One of the principal arguments for Friday is found in Mark 15:42, which notes that Jesus was crucified “the day before the Sabbath.” If that was the weekly Sabbath, i.e. Saturday, then that fact leads to a Friday crucifixion. Another argument for Friday says that verses such as Matthew 16:21 and Luke 9:22 teach that Jesus would rise on the third day; therefore, He would not need to be in the grave a full three days and nights. But while some translations use “on the third day” for these verses, not all do, and not everyone agrees that “on the third day” is the best way to translate these verses. Furthermore, Mark 8:31 says that Jesus will be raised “after” three days.

The Thursday argument expands on the Friday view and argues mainly that there are too many events (some count as many as twenty) happening between Christ’s burial and Sunday morning to occur from Friday evening to Sunday morning. Proponents of the Thursday view point out that this is especially a problem when the only full day between Friday and Sunday was Saturday, the Jewish Sabbath. An extra day or two eliminates that problem. The Thursday advocates could reason thus: suppose you haven't seen a friend since Monday evening. The next time you see him it is Thursday morning and you say, “I haven’t seen you in three days” even though it had technically only been 60 hours (2.5 days). If Jesus was crucified on Thursday, this example shows how it could be considered three days.

The Wednesday opinion states that there were two Sabbaths that week. After the first one (the one that occurred on the evening of the crucifixion [Mark 15:42; Luke 23:52-54]), the women purchased spices—note that they made their purchase after the Sabbath (Mark 16:1). The Wednesday view holds that this “Sabbath” was the Passover (see Leviticus 16:29-31, 23:24-32, 39, where high holy days that are not necessarily the seventh day of the week are referred to as the Sabbath). The second Sabbath that week was the normal weekly Sabbath. Note that in Luke 23:56 the women who had purchased spices after the first Sabbath returned and prepared the spices, then “rested on the Sabbath.” The argument states that they could not purchase the spices after the Sabbath, yet prepare those spices before the Sabbath—unless there were two Sabbaths. With the two-Sabbath view, if Christ was crucified on Thursday, then the high holy Sabbath (the Passover) would have begun Thursday at sundown and ended at Friday sundown—at the beginning of the weekly Sabbath or Saturday. Purchasing the spices after the first Sabbath (Passover) would have meant they purchased them on Saturday and were breaking the Sabbath.

Therefore, according to the Wednesday viewpoint, the only explanation that does not violate the biblical account of the women and the spices and holds to a literal understanding of Matthew 12:40 is that Christ was crucified on Wednesday. The Sabbath that was a high holy day (Passover) occurred on Thursday, the women purchased spices (after that) on Friday and returned and prepared the spices on the same day, they rested on Saturday which was the weekly Sabbath, then brought the spices to the tomb early Sunday. Jesus was buried near sundown on Wednesday, which began Thursday in the Jewish calendar. Using a Jewish calendar, you have Thursday day (day one). Thursday night (night one), Friday day (day two), Friday night (night two), Saturday day (day three), Saturday night (night three). We do not know exactly what time He rose, but we do know that it was before sunrise on Sunday. He could have risen as early as just after sunset Saturday evening, which began the first day of the week to the Jews. The discovery of the empty tomb was made just at sunrise (Mark 16:2), before it was fully light (John 20:1).

A possible problem with the Wednesday view is that the disciples who walked with Jesus on the road to Emmaus did so on “the same day” of His resurrection (Luke 24:13). The disciples, who do not recognize Jesus, tell Him of Jesus’ crucifixion (24:21) and say that “today is the third day since these things happened” (24:22). Wednesday to Sunday is four days. A possible explanation is that they may have been counting since Wednesday evening at Christ’s burial, which begins the Jewish Thursday, and Thursday to Sunday could be counted as three days.

In the grand scheme of things, it is not all that important to know what day of the week Christ was crucified. If it were very important, then God’s Word would have clearly communicated the day and timeframe. What is important is that He did die and that He physically, bodily rose from the dead. What is equally important is the reason He died—to take the punishment that all sinners deserve. John 3:16 and 3:36 both proclaim that putting your trust in Him results in eternal life! This is equally true whether He was crucified on a Wednesday, Thursday, or Friday. - On what day was Jesus crucified?

The following may be of interest to some:

• Why did Mary Magdalene and the other women disciples wait until the dawn of Sunday before arriving at the tomb?

It looks like you are very interested in biblical chronology. Please can I recommend 4 books:- "Babylonian Chronology - 626 bc to ad 75" by Richard A. Parker & Waldo Dubberstein, published 1956 (available for free online); "From Abraham to Paul - a biblical chronology" by Andrew Steinmann, 2011; "Daniel's Seventy Weeks" by Derek Walker, 2009 (Pastor of Oxford Baptist Church, available free online); and "The Mystery of the Last Supper" by Colin Humphreys, 2011. Andrew Steinmann is a great book but mistakenly puts the killing of the Passover lambs on 13th Nisan and so messes up the crucifixion week. This mistake is rectified by reading The Mystery of the Last Supper.

The evidence points to the crucifixion happening on Friday 3rd April AD 33, which was 14th Nisan (Thursday sunset to Friday sunset) according to the conventional Jewish (Babylonian based) calendar.

The meaning of the "third day" is "the day after tomorrow" as can be seen in Luke 13:32 "Go tell that fox.. I do cures today and tomorrow and the third day I shall be perfected." It is also seen in Leviticus 7:15-17, and 2 Chronicles 10:5 and 12.

"Three days and three nights" of Matthew 12:40 must agree with the more common phrases "after three days", "on the third day", "in three days" which must all mean precisely the same thing. Esther said she would neither eat nor drink "three days, night or day" and she stood before the king "on the third day" (Esther 4:16-5:1). But a literal "three days, night or day" would have led her to stand before the king on the fourth day.

Since our Lord rose from the dead on Sunday morning just after dawn then he died on Friday.

To get the gist of the argument see the following two answers:-

Was the Last Supper not the Passover meal?

Why did Mary Magdalene and the other women disciples wait until the dawn of Sunday before arriving at the tomb?

answer deleted by user answer deleted by user

It looks like you are very interested in biblical chronology. Please can I recommend 4 books:- "Babylonian Chronology - 626 bc to ad 75" by Richard A. Parker & Waldo Dubberstein, published 1956 (available for free online); "From Abraham to Paul - a biblical chronology" by Andrew Steinmann, 2011; "Daniel's Seventy Weeks" by Derek Walker, 2009 (Pastor of Oxford Baptist Church, available free online); and "The Mystery of the Last Supper" by Colin Humphreys, 2011. Andrew Steinmann's is a great book but he mistakenly puts the killing of the Passover lambs on 13th Nisan and so messes up the crucifixion week. This mistake is rectified by reading The Mystery of the Last Supper.

The evidence points to the crucifixion happening on Friday 3rd April AD 33, which was 14th Nisan (Thursday sunset to Friday sunset) according to the conventional Jewish (Babylonian based) calendar.

The meaning of the "third day" is "the day after tomorrow" as can be seen in Luke 13:32 "Go tell that fox.. I do cures today and tomorrow and the third day I shall be perfected." It is also seen in Leviticus 7:15-17.

"Three days and three nights" of Matthew 12:40 must agree with the more common phrases "after three days", "on the third day", "in three days" which must all mean precisely the same thing. Esther said she would neither eat nor drink "three days, night or day" and she stood before the king "on the third day" (Esther 4:16-5:1). But a literal "three days, night or day" would have led her to stand before the king on the fourth day.

Since our Lord rose from the dead on the first day of the week, Sunday morning, just after dawn, then he died on Friday.

Those who think there was only one calendar, the Temple (Babylonian based) calendar where days began and ended at sunset should carefully consider Matthew 28:1, Mark 14:12, and compare Mark 16:1 (they bought spices after the Sabbath) with Luke 23:56 (they prepared spices before the Sabbath).

To get the gist of the argument see the following two answers:-

Was the Last Supper not the Passover meal?

Why did Mary Magdalene and the other women disciples wait until the dawn of Sunday before arriving at the tomb?