Following the video on AppliancePartsPros.com, I pried the old part off rather than wasting any more time trying to unscrew it. Before viewing the video, I tried to unscrew the coupler, but I couldn't keep the motor shaft from turning. I even took the case off, but I still couldn't find anything inside that would do that. (The fan didn't have enough grip on the shaft to keep it from turning.)
Had I gone to AppliancePartsPros.com first rather than waiting until I was stumped, I could have saved myself a lot of time.