So I've verified that the Lansing, MI grainger carries this capacitor
and I can buy one on Tuesday. Woohoo!

In the mean time I've found that the motor will actually run fine
provided I give it a nudge to get it started. I guess the whole
purpose of the capacitor is to start the electric motor? How does that
work? I don't actually understand how a single-phase AC current can
turn a motor at all... since there's no rotating magnetic field.

Anybody know of a good reference on how an AC motor works?

Dan