I figured out the problem. The brass sleeve that the choke controls pivot in was glued on, and the glue broke, causing everything to slide around and fall apart. Rather than try and glue it again, I decided to cut a sheet of copper, solder it to the brass rod, and hold the copper down with the same screw that holds the entire mess together. I drove the truck into town and back, and I am happy to report no further choke problems.

https://drive.google.com/open?id=1t6BbLdN5c65e_BzfnkvcZjQltVadBTv4

As an added bonus, because I couldn't be bothered to make it look clean, the copper plate also doubles as a retainer for my electric choke rod, eliminating the need for a clip retainer. Quite convenient. Is mine special in having been glued? I have a second carb, and the sleeve looks more pressed in than glued on.