Well, I think I can rule out the linkage as the problem. I've been over that with a fine tooth comb, disconnected all the rods, put new washers in, tightened the whole shebang, and played with the transmission levers on the side cover as I was reconnecting the rods. There's no more or less play involved whether the rods are on or off. Looks like something's not moving properly inside the tranny, and that's why 2nd isn't locking in place properly and jamming when I try to shift into 3rd.
It's been interesting driving in LA with only 2 gears...
At least the linkage is now tighter than it's been in a decade! There's no excess play in the whole system, and once I get the problem in the tranny fixed, I'll probably have the snoothest running '54 on the block.
... even if it's the ONLY '54 on the block!
Tomorrow I think I'll pull off the side cover and see what's cooking in there. And yes, Stuart, it DOES rain in Southern California. Mostly when it's time to fix something on the truck!