Txbeerman, welcome to the site. Its a great source for help.
I am at this very moment in the throes of the very same quandary as you, although I have been able to get part numbers from dometic, it just takes forever on the phone.
here is what I have.....2 dometic duotherm ac's on the roof, model 630035331....both have heat pumps...both 14 years old....13.5K
a duotherm 5 button thermostat
the same identical control box on both of my ac's as you, 3109226.005
I replaced the front ac with ac model 651816c, 15k. (IM assuming yours is 13.5)
My difficulty was I also bought a control box to 'smarten up' my old ac to be recognized by the new 10 button thermostat.My new ac worked no problem with the new setup, but my old ac, cannot and will not, under any circumstance, according to dometic, be compatible with the 10 button new thermostat. I am right now in the midst of having ordered a control box for my new a/c, model 3313107.107, to dumb down my new ac, to work my new ac, on the old duotherm 5 button, unless I want to run with 2 thermostats and then have to play with the toggle switch settings. As far as what wires connect to what wires, I'm electrically illiterate, but had a buddy do that end of the project for me.
Im going to hold on to my new 10 button, and ultimately, when I have to replace my back a/c, ill be able to run both off the 1 tstat, and remove the control box from the front a/c.....
Hope that makes some sort of sense, if not, feel free to PM me, and ill try to take pictures, and send them....
Best of luck, and again, welcome.
Kevin
FMCA #F383349
2006 Monaco LaPalma
2015 Hyundai Elantra