jadinolfi:
Welcome to iRV2.com!
I'm not quite sure which DuoTherm HP you purchased, there are a couple, only one type of which will work with an analog thermostat. It may also work with the normal house thermostat like the Honeywell. Installation instructions for it are here:
http://bryantrv.com/docs2/docs/operating/bairducted.pdf
As you found out, the other Duo Therm HP's will only work with the Comfort Controls and will require running a 4-wire cable from the unit to the thermostat.
Several people have used house thermostats on RV air conditioners but not heat pumps. Here is the closest I found, it has the same color wires as the manual says it should on P16:
RV Digital Thermostat Upgrade | ModMyRV
It looks like the Violet wire on the HP would be for the reversing valve, which would hook to the O terminal on the thermostat. So the wiring would look like this:
Color on HP diagram - thermostat connection
Violet - O
Yellow - Y
Orange - G - (this will run the low fan speed, if you want high also, hook the blue thru a switch as in the link above)
White - E and Aux (if a furnace is connected to the HP)
Black - R
Please note these are my educated guesses, I cannot guarantee this will work, but should not harm anything if hooked up wrong. If you get heat instead of cool you should move the Violet wire to the B connection on the thermostat.
If the thermostat requires 24VAC to run the relays it will not work. You may be able to use the +12V (Red) wire, but you have a much better chance of breaking the thermostat or Heat Pump if you connect it wrong, and I do not know which terminal on the thermostat to try.
Good luck!
Stewart