Many thanks to Ben for sharing his scanned service manual!
I was able to remove the condenser fan motor, but I see no way to take the housing apart in order to replace its crispy cord. It looks as if the two sections have been pressed together.
I can't find a part number on the housing. Just this: 5K51AL24D. Per the service manual, this is a two-phase motor, and as was stated further up, the cord has three conductors, black, white, and green. They connect to the relay as follows:
Green = Terminal 1, shared with Blue wire from the guardette
White = Terminal 2, shared with White wire from compressor start terminal
Black = Unnamed, possibly AKA Terminal 4 --shared with the power cord and either common or run wire from the compressor, I can't be sure.
New aftermarket replacement fan motors only have two conductors (as seen in Paul's picture). I guess I'm OK with that, and it looks like placement of the holes for the mounting screws is standard. Unless there's a way to get the existing fan motor apart, this may be the best solution for the fan.
Now here's the interesting thing I discovered. When pulling the green fan wire connector off the relay, the whole blade it slid onto was moving around. The screw holding this blade and the wire from the guardette was slightly loose. Could this have been the source of the trouble? It would be just my luck that tightening one screw would have fixed the problem and left the fan and its wiring undisturbed.