I remember in the VW manual for the camper it sort of infers that it is OK
to run the fridge on propane while driving.  In the section about using
propane it talks about being sure the van is relatively level.  It says
that the levelness only applies to when the van is parked, that when it is
moving, and tilts temporarily, that is not cause for concern.

As far as using the 12v mode, I have gone to using an inverter to make 120v
AC from the 12v, and running the fridge on that.  This way I get
thermostatic control, and the inverter shuts off when the battery gets down
to 10v, so I don't kill my aux battery if I am running it parked for a
short while.  I went cheap for the short term and bought the cheapest lawn
tractor battery I could find.  Less than $20.  It will run the fridge for
about 1-2 hours after driving depending on various factors.  That works for
me, for now.

Edward