Jim-
I wish that I could have helped you out with the spare ribs.

Hopefully, the thermocouple will do the trick for ya. If you've had a history of good success with your refrigerator, the thermocoupler might in fact be the culprit as they do degrade with age. My refrigerator on the otherhand has been intermittant since new in the propane mode. My symptoms are that the refrigerator (RM3663) works perfectly on 110VAC and 12VDC, but will "click" off after a couple minutes of operation in the propane mode. The flame is perfect. Definitely sounds like a bad circuit board. The replacement Dinosaur Board goes for about $99 and has a three year warrantee. The thermocouple is so cheap, I figured that it was worth a try. Also, it is probably good insurance to carry a spare.
I have a .pdf document that was submitted to Escapees magazine awhile ago which I found on the web which describes the deficiencies of the OEM Dometic refrigerator controller boards (specifically, models RM2607, 2611, 2612, 2652, 2807, 2811, 2812, 2852, 3607, 3662, 3663, 3807, 3862, 3863, 4872, 4873, 7030, 7130, 7732, 7832). It also explains the fixes that the Dinosaur board has incorporated within their design. If anyone is interested in the article, shoot me an email with your email address (it is only 1-page in length).