Update -- on a road trip, and the fridge is still behaving very
oddly.   Some days it runs all day.  Other days it repeatedly goes
out every few hours or so.    At first I thought it was temperature /
pressure related, but then on the coldest night (20F) it ran all
night, and then the next day it went out when sitting in the sun (70F
+).    Has stayed lit for hours while driving in strong headwinds,
and also gone out when not moving with still air.   Very strange.
Watching the flame through the viewing window, it does look a little
flickery on occasion -- it will burn steady for a few seconds, then a
brief surge with some yellow, then back to solid blue.   The intake &
exhaust were both vacuumed & visually inspected with a flashlight and
looked good, the combustion chamber & jet had some ash / crud in
them  but were clean.  Gaskets etc. in good shape.

Contaminated propane (water or Methanethiol crud in the system?)
Some other problem with the Dometic's pressure regulator or
temperature sensor?