I have the exact same problem with my fridge also.  Same symptoms etc. 
The only thing I can think is that the billows and gas expansion tube
that governs the thermostat is not opening up the gas valve all the way
to get max burn.  If this is the problem shouldn't we be able to  bypass
all of the shutoff valves and thermostats and hook up a propane tank (11
lbs.) right to the oriface to get the max burn.  Theoretically this
should work, right?  Then you could check to see if it is anything above
the oriface.  Then keep stepping backward past each part.

Lets keep bouncing ideas off of each other.  I've been working on this
one for months too.

Blake Heinlein
83.5 Westy "Toaster"
Don't have a dog for my van yet!