First, let's tighten the scope. Pontius Pilate ruled Judea from mid-26 until mid-36 AD. Jesus' baptism dates to 28 or 29 AD. Jesus' public ministry ran between 2 and 4 years. Saul of Tarsus met Jesus Christ on the road in early 34. Challenge any of those points if you dare, but accepting them all leaves four possible years for the crucifixion.
Granting that Passover Night is still going to fall on or within one day of the full moon, in March or April, the options for the Passover Night between 30 and 33 AD are as follows:
30 AD: March 8th, Wednesday (+) or April 6th, Thursday (+)
31 AD: March 27th, Tuesday (+) or April 25th, Wednesday (+)
32 AD: March 15th, Saturday (+) or April 14th, Monday (+)
33 AD: March 5th, Thursday (+) or April 3rd, Friday (+)
All dates as found on the Julian Calendar; Source: Time and Date AS (Stavanger, Norway)
At first glance, we have four of eight full moons that fall within one day of Friday. Now, we begin to eliminate. First, we note that 31 AD is completely out. Second, we note that March 5th and 8th are almost certainly too early for the Sadducees to have scheduled in advance, as they would have been in the lucrative habit of doing. This leaves three years to reckon with.
The year 30 AD only works if we posit a two year ministry for Jesus, which is extremely implausible. The year 32 AD is very doubtful because either moon date was viable, and the Sadducees would have been much more prudent event planners to select the April moon many months in advance.
That leaves April 3rd of 33 AD, with a Passover Feast on Friday, suggesting that the careful night sky observers really must have been doing their jobs well - as they most likely should have been. Perfectionists can protest all they want, but the balance of evidence and all our best reasoned considerations very strongly suggest that this year is the start of chronology for Jesus Christ's ministry.
Working backwards, Luke's date on the Lord's baptism (28 or 29) is best fixed by determining whether Jesus' ministry was more likely three or four years in length. On that note, search this site for "28 AD", and also review my post on Chronology of the Gospels.
I should so be charging you people money for all this. ;-)
Note: Obviously, these are not absolute, airtight arguments. Historical ones rarely are. However, I contend these are good arguments, presenting the most likely conclusions. They are probably correct. Anyone willing to proceed with historical reconstruction of Christ's public life should begin here. But any faith-based scholarship which refuses to start somewhere, or which prefers an ahistorical view for some reason, is being an irresponsible caretaker of scripture's facticity. IMHO. History is what it is. Reconstruction is worth what it's worth. Let's work with it.