Heating Question (Cycle on and Off)

I think your cycling on and off is due to heat loss. Do you have a digital or analog thermostat ? We have 2 different TT's (see my signature) and the Jayco has a thermal package and does not cycle on nearly as much as the Shasta. Both have digital thermostats. Keep in mind the furnace blower will run before the burner ingnites and continue to run after the thermostat is satisfied. This is for safety to cleat any LP gas in case the thermocouple or electronic ingnitor fails to prevent a gas explosion.
You may want to try a small electric heater to supplement the gas furnace and take the extreme chill out so the furnace can keep up.