The issue really isn't a big deal when we look at Judaism at the time of Jesus.
There were different sects in Judaism. Some sects used a solar calandar and some used a lunar calendar. These celebrated the Passover on different nights. There ware clearly divisions in the liturgical calendar across sects.
The Sadducees were the high priests and were in charge of the temple. These used the lunar calendar in which the feasts fell on different days each year.
Essene and Qumran Jews however, used a solar calendar where the major festivals fell on the same day of the week year after year. For Essene and Qumran Jews, passover was always after sunset on Tuesday night. The site of the last supper is in the Essene section of Jerusalem. Jesus was likely an Essene Jew. Essene means "Holy Ones" and they had a very monastic spitituality, like Jesus who often went off into the desert to pray.
As an Essene Jew, Jesus would have eaten the passover on Tuesday evening but he later stood in the praetorium where the Jewish authorities (Sadducees) did not enter (John 18:28) so as not to defile themselves for their own passover, which was Friday night.
It's not that big of a deal when we realize how these people lived every-day life.