A hint: Since you have turned off the propane at the source and tried to fire up the furnace in your testing, it would be a good idea to turn on the propane then light the gas stove. Why? There is a very good chance that there is now air trapped in the propane system and lighting the gas stove for 5 minutes will purge most of it out. The furnace is very fussy about the propane/air mix whereas the stove is not.
After purging, when you try and light the furnace, do you hear a series (up to 3) clicks coming from the furnace?? (This is the igniter/flame detector trying to light the propane.) Do you smell propane around the exhaust port??
After 3 attempts to light (clicks) the furnace ignition circuit is locked out and the furnace has to be reset before another attempt is made. (Reset= turn the thermostat to a much lower temperature for a few minutes before trying again.)
For the thermostat, Coleman Mack RVComfort is the brand but the model # is likely found under the cover which likely just pops off. The manuals for the thermostat are available on line; Google RVComfort.