The mother of invention may be laziness, but also a good portion of determined thrift. The part at the local appliance store was 75 dollars and a few days' wait. Figured I'd just use my rigged one as is until I buy a new fridge.
On a whim I stopped at the scrap yard on the drive back and looked at the dozen or so fridges on the lot. The relay is just a snap-in that's exposed in the back of the fridge.. 15 second removal tops. There were two of them with identical part numbers heading for the heap. I snapped them off and gave the attendant a buck for them.
Snapped one in when I got home and all is golden. Good for another few years anyway.