a day for the crucifixion

I want to ask about John 12:1 and 12:12. In the first verse we see that Jesus arrived at Bethany, and we are told it was six days before the Passover. The second verse says that Jesus made his entry to Jerusalem the next day.

Given that Jesus presumably wouldn't have travelled on the Sabbath [Exodus 16:29 seems to forbid this], then we are left with a choice of the two travel days being a Thursday and Friday before the Sabbath, or a Sunday and Monday after the Sabbath.

Counting forward the six days to the Passover, these two possibilities would mean that the crucifixion was on either the following Wednesday or Saturday.

Ruling out the Saturday option as unworkable, we are left with Wednesday, which I don't mind [I don't have a dogmatic position on whether the crucifixion was Wednesday, Thursday or Friday], but it leaves me with some questions.

First, what is your spin on the Wednesday option?
Second, why did the women wait until Sunday to embalm Jesus' body when they could have done it on the Friday [a normal working day in this scenario, as the Thursday was the Sabbath of the first day of the Feast of Unleavened Bread]?
Third, for 3 days and 3 nights to pass since his death, Jesus would have had to resurrect sometime between 3PM Saturday and dawn on Sunday when he was first seen - was he twiddling his thumbs during all those hours?

The real essence of my question has to do with the two verses, John 12:1 and 12:12. Quote: 'Jesus came to Bethany six days before the Passover,' and quote: 'On the next day....Jesus was coming to Jerusalem.'

In short, these two verses place the Triumphal Entry into Jerusalem as being 5 days before the Passover/crucifixion.

Counting 5 days backwards from the choices of a Wednesday/Thursday/Friday crucifixion would mean a Triumphal Entry as being one of these: Friday/Saturday/Sunday.

The Saturday/Sunday possibilities don't work because either one would both have Jesus travelling on the Sabbath. Which leaves us with the Friday Triumphal Entry, which in turn means a Wednesday crucifixion.

For my part, I am not happy with a Wednesday crucifixion, as I think it causes other problems, particularly with the count of days [as well as some of the details, like Jesus returning to Jerusalem the next day, on the Sabbath] between the Triumphal Entry and the Crucifixion described in the other gospels, as well as too many hours being dead, and the delay by the women in embalming Jesus.

Certainly a Thursday crucifixion fits better for various reasons. But I can't reconcile a Thursday crucifixion with the two verses above.

Perhaps someone else has some useful thoughts on the matter to offer.