While I have my own reasons for looking at TNG somewhat dubiously some of its dating references were of help in working out my own chronology.- I didn't accept the 2266-70 time for the five-year mission but rather placed it starting sometime in mid 2271 and ending in late 2276.
This works. I didn't agree with Okuda's explaination that he set TOS in 2266 simply because it was 300 years after 1966.
Using Data's date of 2364 for the first season of TNG makes more sense anyway, because it falls under another one of Okuda's stated rules, using onscreen dates as "offical".
2364 - 78 years = 2286. That's about ten years after the 5-year mission era (by my reckoning) or right in the time of the movie era. Curiously this puts TMP occurring around 2279 or 300 years after 1979 and TMP's release.

When a reference is something like fifty years ago or two centuries ago or three hundred years then that's something you can fudge to make things fit because you can assume the reference is an estimate or a rounded off figure. A figure like 11 years or 13 years or 18 years or 78 years or whatever is too specific to fudge.