You are correct in stating that there was a full moon during the last supper. What is the Bible account for the proper way to determine when the Jews were to celebrate the Passover?
Exodus 12:2 This month shall be unto you the beginning of months: it shall be the first month of the year to you.
“This month” is the Jewish month Nisan which begins at the FIRST new moon following the Spring Equinox. From this Jewish New Year, we can count to the Passover.
Exodus 12:6-11 And ye shall keep it up until the fourteenth day of the same month…(vs. 11)
it is the LORD'S Passover. (As you know, 14 days after a “New Moon” will always be a Full Moon” as you stated.)
Summary: Passover is 14 days after the first New Moon after the spring equinox.
Note: Passover is NOT necessarily the first full moon of spring. Look at 2016. The Spring Equinox for 2016 is March 20. The first full moon after the spring equinox is March 23, but that is NOT the date for the Passover. From March 20, we need to wait for the FIRST new Moon (which is April 7) for the beginning of Jewish New Year. From April 7, we count 14 days which is April 21 for the correct day for Passover (or April 22 using Jewish reckoning of their day beginning in the evening). This does not happen every year, but for 2016, Passover is during the Second Full Moon of spring.
Second Note: Our Lord was crucified in AD 33. In that year, the new moon was March 19 and Thursday, April 2nd. was Nisan 14, 33AD. See astropixels.com for the astronomical dating.