PhD musicologist here, for whatever that's worth, although not a temperament specialist; in fact I find the subject very dreary.
But - for what it's worth - a very important point is Julian Money-Kyrle's, that the organ builders had their own temperaments, and most of the discussion we see was for stringed keyboard instruments. There are a few exceptions such as Werckmeister, but he spent some time lamenting the fact that he couldn't get any builders to adopt his proposals (some of which were rather stupid).
Some random points. Bradley Lehman's temperament met with a lot of skepticism by temperamenters when first introduced, and has now by totally discarded. Here's one refutation:
https://my.ptg.org/blogs/fred-sturm/2014/10/24/lehman-bach-tuning-refuted. It doesn't sound very good to me; it favors the flat keys over the sharps, but every known Baroque temperament (except equal) does the opposite. The final nail in the coffin was that Andreas Sparschuh, who had made the original suggestion that the squiggle on the manuscript of the Well-Tempered Clavier represented a temperament, finally admitted that he had intended it as a joke.
We know that Bach didn't use meantone temperament at Leipzig. There is the anecdote about him torturing Silbermann by playing a long chord on one of his instruments until Silbermann couldn't stand it any longer. Also, and less anecdotally, organs were typically tuned a tone higher than other instruments. Many organs had a gedackt or two at the lower pitch for continuo use, but the organ at Thomaskirche didn't, and Bach had transposing parts for the organist copied out. So there must have been something vaguely approaching equal temperament there. Of course, most of Bach's surviving organ music predates his Leipzig career.
We just don't know about Buxtehude. Based on Ibo Ortgies' research, Kerala Snyder withdrew her suggestion that he would have used something like Werckmeister III. Many mean-tone organs were fitted with split sharps, so that you had two different keys available for, typically, d-sharp/e-flat and g-sharp/a-flat, but the organs at Lübeck didn't. It's possible that Bux's organ works weren't intended for the organ, but as sort of study pieces that were played, if at all, on the (pedal) clavichord. There's the even worse possibility that the problematic pieces, or at least the problematic sections, weren't written by Bux at all, but by some organists in central Germany a generation later, since that's where the sources come from.