2245 represents a logical extrapolation that allows for both the events of The Cage and having time for a Robert April command that was alluded to in The Counter-Clock Incident working backwards from the 2364 date. It was Roddenberry who said that TNG took place 78 years after the current Trek movie at the time (The Voyage Home). Lets be honest, it's easier to come up with a fudge for 'Class of 78' than it is for 2364. Just like it's easier to fudge 'two hundred years ago' than it is to fudge the 1996 date Spock gives for the Eugenics Wars.
Are the chronologies/encyclopedia's perfect? No. But in the broad strokes they work well enough.
About starship registries, I got to tell you that I honestly don't care about them. They're in the encyclopedia, I glanced at them once about twenty years ago and haven't since because they simply aren't important to the stories being told on-screen.
Actually if you Really want to know where Class of 78 comes from, it's FASA, the Spaceflight Chronology universe which was, at the time, fully licensed by Paramount and pumping stuff out for them... Don't believe me? Checkout their TNG Officers Manual or sourcebook for TNG RPG... It sets TNG around the turn of the 24th Century (which not too surprisingly ties into all the TV ads about "The 24th Century is coming or is here" for "Encounter at Farpoint" way back when in the 80s)... In other words, Data graduated in 2278 A.D. going by that timeline...