Replacing the capacitors and relay worked for about a month, but the control board had to have been pretty far gone anyway, as the fridge would never go on a defrost cycle. So after about 10 days the coils would freeze up. I emptied everything again, pulled the freezer apart, defrosted the coils with my heat gun and installed a new thermostat and fan. Same thing happened 2 weeks later.

I bit the bullet and bought the 'service kit', which was a replacement for the original control board (and apparently what is being used to fix all the refrigerators with this problem). The cheapest I could find it was about $275, but it was being drop shipped from the west coast and would take a week to get to the house. So we pulled the coolers out once again, got some dry ice, and toughed it out.

Replacing the control board itself wasn't too difficult. It was pretty much a plug and play solution. The design was interesting though. Whereas the original control board was just one PCB, the new setup was made of 5 separate PCBs. The case that the PCBs was designed to mount to the same spot as the original, but it was much larger, so the fit was super tight. I managed to wrangle it in there, but the rollers on the fridge looked to be jammed and scratched the floor when I moved it back in the place.

2 years later the fridge has been rock solid and the temps haven't budged. Cost a little more than I wanted, but less than having a repair man come out and MUCH less than a new one.