So: Bike's back in operation; they replaced the transmission shaft and several gears. Those have grooves in them, and some of the dogs are worn. I'll post pictures. Stacy at Hillsboro Motosport did a great job tearing it down, replacing parts, and re-assembling. I went for a 200-mile ride after getting my bike back, and it is like a new bike.
Officially what happened is that the shift drum and transmission shaft bearing keeper plates had loose screws, allowing both to float, and parts to wear against each other. Those plates are held in by small screws for which the torque spec is 30 inch pounds (2.5 foot pounds). Threadlocker is specified for those screws, and my suspicion is that this step may have been missed.
I'm thinking this is an original assembly error (maybe break time intervened between operations) and I won the anti-lottery. I'm asking Mother K to help; we shall see. I'm looking for lots of trouble-free miles now; I had the valves set to their outermost tolerance (and I'm pretty gentle to the bike) so that should be good for years.
I guess the lesson from this is - if the clutch play begins to vary - consider that things may be loose inside. This will probably never happen to you.
Glad to be back!