Turns out it's a 4-digit serial early Corp with a quite well-done K swap, obviously taken from a stock '90s 36K. As for why someone did this, and then decided it wasn't worth keeping, is up to the trombone gods to understand.
As it was, it played very well. My only gripe was that the stock 36 slide width is just narrow enough to be quite uncomfortable with a K valve- much like adding something larger to an 88H, it needs a bit more room. I had Benn Hansson add a Shires wide .525 crook, bringing the slide up to 42 width but not adding any wildly different characteristics to the response. It did make it sound just a titch larger, a little more of the depth of a 42 but still easier to play.
Some work remains to be done... the K valve won't come out of the casing, which needs to happen to clean it thoroughly, and there's a popped solder joint from the F wrap to the main bell brace.
However, I'm very happy with the result, especially with my perfectly-matched Doug Elliot setup- XTn104.F+.G4, like a 3GS in Bach terms. I've gone through a couple 36s and none of them felt like they made this interesting of a sound or did it quite so well. Someday I may even get to play it with others!
A comparison to the stock 36 width-
