I've had these mystery buzzes and strange sounding strings in the past. Some still unsolved I even had a guitar recently where one string would have the 12th fret harmonic over the 13th fret almost. (turned out it wasn't my sloppy building, it was the string itself). But I never had an issue this severe so I can only imagine how frustrating it must be..
Here's my suggestion: you have to make sure if this is the following fret(s) that's buzzing or something else. (bridge, fret seated loose, truss rod resonating, flat crown) I know you checked all those things, so all evidence would point to "following fret"... Including having no buzz on the last fret. But if it was that, it should go away when raising action, so there's our mystery right there.
What I'd try: pull out just the last fret, see if the last-1 fret still buzzes. Maybe continue for a few more frets. If the buzzing disappears, then we have a problem with neck-string-fret geometry. If it doesn't, then it's something else.
I measured some guitars that I have at hand and in general the way they're set up is that when I fret a note at the 12th fret, the clearance between the unwound strings and the 13th fret is around 0.10-0.15mm (.003-.004 inches) with no buzz