Down at the tale of the Sigillon discussion, I referred to a page explaining the way the Jewish calendar now works. There's a point there which could use some expansion.
Back in NT days, the Jewish calendar worked like this: on the 30th day of the last month of the year, observers went out to look for the crescent moon. If they saw, that was the first day of the next year. If not, the day after would be the first day. In addition, they would add one day if necessary to keep the new year from starting on certain days of the week. Based on where this day fell in the year, the Sanhedrin would add a second Adar (month in late winter) to keep the feasts in the proper seasons.
It should be noted that the date of Passover is a secondary date in this; the date that they were trying to set was Rosh Hashanah. In particular, they were not trying to make Nisan 14 fall on the first full moon after the vernal equinox, so that when they went to a mechanical calendar, it didn't always fall that early in the year.
That's the biggest reason why the paschalions produce dates which don't line up with Passover in the way one would expect: the "first Sunday after the first full moon after the vernal equinox" doesn't always produce the right date for Passover.
As long as all the various calendars produce the same full moon dates, there is no chance that Easter and Passover will ever be celebrated on the same day. I don't think they do produce the same full moon dates, however. In 2006, for instance, the Dionysian full moon is four days late. In 2019 there is no agreement at all as to which date the full moon falls on; I'm guessing this is an offset year in the Jewish Calendar, which explains the one day descrepancy between the Gregorian and Jewish calendars. The Dionysian date is five days late, but actually, the Gregorian date is a month late!