This is a "Wild Mass Guess" entry, where we pull out all the sanity stops on theorizing. The regular entry on this topic is elsewhere. Please see this programme note.
Looking back at the Book Ends trope, remember also when Sam opened the bar? There was a kid/teen who walked trying to convince Sam he was old enough to buy a beer. Now go forward eleven years to the end where some guy try to walk in, but Sam says the bar's closed for tonight. What if that guy was the same kid from the first opening, now actually old enough to have a beer and finally enters in Cheer once again?
If the kid was 10 or above in the first episode, he'd be the right age in the finale.
In "The Last Picture Show", a former owner takes on Sam's duties for a night, and, upon meeting Woody, remarks "This must be Coach's boy." Bearing that in mind, is it not possible that, somewhere along the line, Pantusso DNA mixed with Boyd DNA and the result is that Woody is, in some small way, Coach's boy?
Consider the following: Their personalities are very similar, they are both thick as mud (bad genes perhaps), and the fact that Coach was the only person who wrote back when Woody was looking for a job may denote a correspondence between long-lost relatives.
Except that it's outright stated that Coach's dementia is not natural but due to taking one too many baseballs to the head.
Except that it is also outright stated (near the end of the 3rd season while Coach was "away") that Coach's sister suffers from a similar affliction. I doubt she took too many baseballs to the head.
The faux-Sam actor in Diane's play (in her Frasier episode) is Lance Apollinaire, the "Greek-God-like" student she almost fell for in "Knights Of The Scimitar".
He certainly looks and sounds kinda like him...and there's also Diane's exchange with him....
It all takes place on a holodeck.
Now, stay with me. See, all the characters drink all that beer and suffer no real ill-effects. It's obviously synthehol. Norm, is of course, Morn from Deep Space Nine visiting other friends. And Captain Bateson likes to play the part of a nuerotic psychatrist. And there's that long-lived Vulcan officer who took a turn playing the hysterical human woman who 'owned' the bar.
Sam and Diane get back together after Diane's appearance on Frasier, but before Woody's.
FIRST—Sam's vision at the end of "I Do, Adieu", after Diane leaves. The extended vision earlier in the episode shows Old Sam as very lethargic and unwilling/unable to move for too much, leaving Old Diane to basically do everything. While their marriage is happy, it isn't particularly passionate. However, in the episode's finale, we see Old Sam up and active, and dancing romantically with Old Diane.
The implication: The first vision is the future stemming from Diane not having a successful career (as is pointed out in dialogue between the old couple). While their love is preserved through the years, Diane's fears from "Coachie Makes Three" of their relationship becoming "routine" and ultimately dull is realized. In the last vision, their passion lasts with their love—as when Diane finally comes back to Sam, they are both more aware of their own potential—what they have, and what they truly desire in life. Thus, Diane leaving ultimately leads to a more fulfilling marriage, in the future.
SECOND—The Rebecca-era episode "Go Make" foreshadows that Sam will marry and have a son "in a few years"—just not with Rebecca.
The last time we see Sam, in his appearance on Frasier, he is single—but the episode ends with a hopeful exchange between him and Frasier....
Note carefully that exchange, as Sam recovers from having broken up with his fiancee due to her having slept with Cliff, Frasier tells him flat-out that that reason was obviously an excuse. Giving Sam a pointed look, he adds, "We both know there were more compelling reasons...."
THIRD—Diane's play in her own Frasier episode is a not-so-subtle spoof of Cheers—one that emphasizes the Sam/Diane romance. Diane herself shares a passionate kiss with the "faux-Sam" actor.
In the end of the episode, she notes to Frasier that she is putting the breaks on the production, and returning to Los Angeles to (she implies) basically re-think her life. It's a good bet she's been shocked by Frasier's earlier outburst into taking a hard look at herself—and the fact that she hasn't gotten over Sam at all...to the point of having fallen (however briefly) for a Suspiciously Similar Substitute.
FOURTH—When Woody shows up in Seattle, he gives a rundown of what the gang is doing in Boston. All he says about Sam is "Sam's doing great!"—while going into a bit more detail about the other mains.
It's possible Woody doesn't have an answer as to why Sam's doing so "great". Sam's smilingly tight-lipped about it.
Perhaps Woody DOES know—and is cleverly able to keep a secret, revealing some Hidden Depths in the usually slow-witted Woody.
Put it all together, and...
Sam and Diane are having a charming "scandalous affair" that the gang knows nothing about, involving Sam using various excuses to cover for his annual visits to Los Angeles—and Diane. (The secrecy's part of the thrill....) And they won't reveal it to all until they agree it's time to tie the knot—which they will, post-Woody's-episode.
Actually, this fits quite well with the Frasier Season Seven episode "Hot Pursuit", which has Frasier just returned from a visit to Boston...and suddenly reflecting on the fact that he's alone, and currently without much of a love life. In hindsight, Fridge Brilliance: In addition to visiting Frederick, he was in Boston for Sam and Diane's wedding!