Signed up at Appliance blog Repair Forums and started asking dumb questions.
One of the regulars said that the resistance I was measuring across the PTC relay was way too high (about 470 ohms) so I took a chance and ordered the part.
The fridge is working now.
The question below re: How Long Did the Project Take? It took a few hours of asking questions, checking parts with my multimeter, trying to educate myself, etc. The actual repair (replacing the bad PTC relay with a good one) only took a few minutes.
I took pictures with my phone during disassembly so I didn't screw up.