m kinsler writes:

I like to have an excuse to dig out my old coil winding machine that I
brought back to working order from a seized rusted mess combined with mice
nest that was in a leaky shed for decades.

That explains a great deal right there. Otherwise, motor rewinding is
a difficult and obscure art, at least for most of us. I've been
building electromagnets for demonstrations at the science museum, and
it doesn't take long for even the simplest coil to turn into a mighty
mess if you're not careful.

I have a vacuum pump that's essentially integral with its squirrel-
cage induction motor, and the stator overheats. The fellow at the
motor shop gave me some insane estimate of several hundred bucks to
rewind the thing; I'm ready to try it myself.

That will likely not be fun, winding machine or not!

How badly/quickly does it overheat?

I assume you're sure it's set for the correct line voltage, if that's
changeable.

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