Once I had a chance to really look at it, on his ultranifty and hyperkeen workbench, I could see he was right. There's a crapton of play in it; even though it's not that noisy, the play alone could be the source of my death wobble.
...the U-joint was $9, as advertised. Og replaced it for me, since he's got a vise that's big enough, and he's done it before; I helped as much as I could and learned much about the replacement of U-joints. I have a picture (which I'll upload later) of just how done that U-joint was. Suffice it to say that when the grease has turned brown and the consistency of clay, it's not terribly surprising that the bearing in question does not move freely. Holy crap.
Og said it was a testament to the strength of hardened steel that it hadn't simply broken. This u-joint did not suddenly get like that last week; God alone knows how long it's been gummed up like that, and I've been driving 60-70 miles an hour routinely.
I don't expect the driver's side to be in much better condition, but that will have to wait until I have the money for the parts. The hub is a Timken bearing, and ironically it was the cheapest one AutoZone had. The U-joint was another ten.
Getting to Og's place--I'd put the bike on the charger as soon as I got home, so I was able to ride it; but how to get sixty pounds of axle shaft there?
I should have taken a picture: my solution was to tie it to the side of the bike. The differential end got lashed to the swingarm, and the u-joint end got tied to the highway bar on the right side. I put a rag between the shaft and the engine housing, and that way it just gave me enough room to put my foot on the foot peg and operate the rear brake. It probably looked pretty silly, but it worked.
Og volunteered to follow me home, once all the banging and stuff in his shop was done, and bring the parts with him, so all I had to carry was the old u-joint and the battery charger I'd brought with, so I could recharge the bike's battery while we worked.
Anyway, it's all reassembled, but I'm waiting for daylight to take the shakedown cruise. Further bulletins as events warrant.