Thanks for the comments, folks. I left the spindle swimming in penetrating oil for several days, then I went back out and tried the suggested methods of removing the chuck.
Alas, it is stuck. As in, stuck. I really can’t get it loose with one hand on the spindle and one hand on the chuck - I need to have the spindle locked good and solid so I can work on the chuck with both hands. Unfortunately, this lathe does not have a spindle lock, but thanks for suggesting that. Also, I don’t have a machine shop - this lathe is the only such machine I have, as I’m set up almost wholly for woodworking, so I can’t readily fabricate metal tools. Otherwise I’d make an adjustable wrench with three nubs that could clamp down completely around the spindle. That would immobile the spindle but good!
As it is, I’m resigned to taking apart the spindle assembly so I can remove the spindle and chuck from the lathe. Then I can put the spindle in a padded vise and have both hands free for the chuck. I have an exploded diagram of the spindle assembly, but I would appreciate any tips on the disassembly and re-assembly process. I understand there‘s a potential issue with reinstalling the bearings, and there’s a key on a shaft somewhere? I can just picture myself cussing as I hear an unseen something fall off inside the housing…