I read the stories on the website here and found the timer on the freezer and manually rotated the gear that should be turning normally by the timer's internal motor. At some point while I was rotating the timer (clockwise) manually, I heard a 'click', and at that point, the compressor turned off, the internal fan stopped running and the defroster heater turned on. I verified that the defroster was working by looking at the drip pan at the bottom of the freezer and I saw water dripping a few minutes after I had rotated the timer by hand.
I bought a new timer from AppliancePartsPros.com (here) and got it in two days.
Unplugged the AC cord of the freezer, removed two 1/4" hex screws with a nut driver, unplugged the four-prong plug on the timer and installed the new timer in five minutes
The freezer is now frost-free again and getting down to -20 degrees!