Well, RIP this motor (gory photo below).
The screw on the end cap was very short, maybe 3/8" or smaller. It was just plugging up the hole for oil/grease.
The shaft was absolutely not coming out. I wasn't able to get anything under the disc with enough leverage to lift it, and I suspect there was something misaligned/jammed/just not right with the mechanism that led to it's catastrophic failure.
I took BeerHippie's advice and squirted some CRC contact cleaner down in there and called it a day. I already had repainted the top cap and the collar and it was looking nice. I figured I would paint the bottom cap once everything was back together to avoid spraying any of the internals that I couldn't remove.
Unfortunately, as I was tightening the nuts on the four threaded rods that pass through the motor, there was a sudden BANG and the motor jolted. I thought at first that this was just the collar snapping back into place, but suddenly the shaft was completely stuck. Even after taking everything apart again, I couldn't spin it even with pliers.
I took a look at the back of the motor, and saw this:
I have truly no idea how this could have happened just by tightening the nuts that hold everything together. I was even tightening them all gradually in an X pattern so that the force would be fairly even as the housing came back together. Something internally must have been very misaligned or perhaps something foreign was jammed in the starter switch that I couldn't see or get to.
In any case, time to try and source a replacement motor...