Ah, but you're forgetting that "the most recent adventure of Kirk and Spock" had no canonical date of its own more specific than "In the 23rd century" (from the start of TWOK)... and that most fan chronologies of the time placed the TOS/movie era sometime in the early 23rd century, inasmuch as evidence ("Space Seed," "Tomorrow is Yesterday," etc.) suggested it was closer to 200 than 300 years in the future. If the FYM was c. 2207-12, and TWOK-TSFS-TVH c. 2222-23, then TNG would have begun c. 2301... at the very start of the 24th century. This would appear to have been the original intent, based on the 1987 version of the TNG writers' guide (by Gerrold & Roddenberry), which explicitly stated the show was set "near the beginning of the 24th century." Thus, if Data was (re)activated 26 years prior (as we know), and promptly entered Starfleet Academy, he could easily have been part of the class of '78. It all fit together just fine... until somebody inserted "2364" in the script of "The Neutral Zone" at the end of season 1, and everything had to be recalculated.
I'm partial to that explanation, as it would smooth over a multitude of sins, but I'm not holding my breath to ever see it confirmed canonically...
You might think that, right? But... I live in Richmond, VA, where until quite recently a major boulevard was lined for over a century with massive statues glorifying Jefferson Davis, JEB Stuart, Stonewall Jackson, and other Confederate figures, all of whom fought a losing war to preserve human slavery, unequivocally on the wrong side of history, against the very country the statues are situated in. Go figure.