The apparent contradiction is not that hard to resolve. The different parties in Judea and Galilee at the time observed the calendar differently, one starting the day at sunup the other at sundown. With all the pilgrims in town for Passover, the leaders did not try to reconcile it, because it allowed the priests two days to get all the sacrifices done.
Clearly, the synoptices used one calendar, while John used another.
A lot people believe He was actually crucified on "good Thursday" instead of Friday, because they suggest there was an extended sabbath for Passover. I don't know, but that is what some believe.