The selector is moving, but I haven't been under while the engine is
running.  I didn't hear any difference when I moved the shifter, but that
was with me sitting in the vehicle.

Sounds like rebuilding the tranny myself isn't worthwhile, and I have to
save up till someone experienced can replace the tranny with a
genuinely-good one.  Don't think I can face pulling it out on the chance
that the shaft might be wrong, only to reassemble and find that wasn't the
problem and the thing is still immobile.