It is true that no one can get three days and three nights (as clearly taught in Matthew 12:40) between Friday evening and Sunday morning. Those who say partial days may count are still not being straight. There are only two nights no matter how you count. Those who claim this also teach that Sunday counts as a day. However, John 20:1 teaches that the seplechre was empty before daylight. Certainly, there cannot be three days and three nights between late Friday afternoon and before dawn on Sunday. This is a tradition that lacks biblical support.
For years, I taught that Wednesday was the day of the crucifixion and still hold it out as a possibility. This way, it is easy to get three whole days and three whole nights. However, about a year ago I came across a couple of problems with this interpretation. First, this approach requires Jesus to rise from the dead before He remained a fourth night in the grave. Using Roman reckoning, He would be there Wednesday evening, Thursday evening, Friday evening, and Saturday evening. The solution is to have Him arise as evening begins on Saturday night. However, this does not go well with statements of scripture as to the time of His resurrection. He seems to have risen shortly before dawn. I do admit that the wording might allow for an earlier rising, but it is still a problem.
Another problem that bothered me even more was the statement of the two disciples on the road to Emmaeus on Resurrection Sunday when they unknowingly walked with Jesus. They said of Jesus, "But we trusted that it had been he which should have redeemed Israel: and beside all this, to day is the third day since these things were done" (Luke 24:21). Now the third day might or might not include the first day. That is, Friday might be said to be the third day from Wednesday (Wednesday, Thursday, Friday) or Saturday might be said to be the third day from Wednesday (from Wednesday to Thursday, Friday, Saturday). However, I cannot imagine how Sunday could be the third day from Wednesday. Depending on how you count, it would be either the fourth day or the fifth day, but not the third day.
For these reasons, I am now leaning more toward Thursday being the day of the crucifixion. It is the fifth day of the week (a number often associated with death in the Bible). It would satisfy Sunday being called "the third day since these things were done" (as in Luke 24:21). It would also allow for three days and three nights, although not necessarily 72 hours (something I do not think is required by the statement in Matthew 12:40). The nights would be a partial day on Thursday, then all day Friday and Saturday. The nights would be Thursday night, Friday night, and Saturday night. I think Thursday would satisfy the statements of all the scriptures involved.
Finally, you mentioned the scriptures that are often used as a proof that Jesus had to be crucified on Friday. The Jews were determined that Jesus be buried before the sabbath that followed the day of preparation (Luke 23:53-54; Matthew 27:62; Mark 15:42; John 19:31). Since the sabbath is on Saturday, then He must have been crucified on Friday. However, two things need to be carefully noted. First, this sabbath was after the day of preparation. This linked it to the annual feast of the Passover. The fourteenth day of the first month at even was the Lord's Passover (Leviticus 23:5) and was a day of preparation. The next day, the fifteenth day, was the first day of the feast of unleavened bread. It was an annual sabbath (more on this later).
Second, this day that was so important that Jesus needed to be buried before it came is called an high day--"for that sabbath day was an high day" (John 19:31). It was not a normal sabbath; it was one of the annual sabbaths. Most Bible teachers make this annual sabbath also the weekly sabbath, but this is not necessary. A weekly sabbath was always on Saturday. However, an annual sabbath could be on any day of the week. This was because an annual sabbath was connected to a date of the year. And, just as anyone's birthday is not always on the same day of the week, so these annual sabbaths occurred on different days.
Where do we get the concept of annual sabbaths? We get it from scripture. In Leviticus 23, the chapter that gives the original feast days for Israel, we see some special days being called sabbaths. "In the seventh month, in the first day of the month, shall ye have a sabbath" (Leviticus 23:24). Leviticus 23:39 says of the first and last days of the feast of tabernacles: "Also in the fifteenth day of the seventh month, when ye have gathered in the fruit of the land, ye shall keep a feast unto the LORD seven days: on the first day shall be a sabbath, and on the eighth day shall be a sabbath." Therefore, the feast of trumpets and the first and last days of the eight-day feast of tabernacles are all called sabbaths. However, these days are connected to calendar days of the year. Therefore, they will vary as to what day of the week they occur. So, they are annual and not necessarily weekly sabbaths.
The requirement for an annual sabbath seems to be that it is called an holy convocation and no work ("servile work") is to be done on this days (just like the weekly sabbath). This brings us back to the day of Passover (the 14th) and the first day of firstfruits (the 15th). The fourteenth day of the first month is not called a holy convocation. Therefore, work can be done on that day (we suppose work like crucifixion). However, though the fifteenth day of the first month is not specifically called a sabbath, it meets the qualifications and therefore is an annual sabbath. Of this first day of the feast of unleavened bread, the law says, "In the first day ye shall have an holy convocation: ye shall do no servile work therein" (Leviticus 23:7). No doubt, this is the sabbath that so troubled the Jews concerning the burial of Jesus. This leaves the door open for the weekly sabbath and the annual sabbath to be on different days. And, since there is no possible way to get Jesus in the grave for three days and three nights between Friday and Sunday, that is clearly the correct answer.