Are there other trees which will survive in your biome which can be coppiced or pollarded? I'd think those would be very valuable techniques in this situation, keeping the precious deep roots of the mature tree while still harvesting fuel. Looks like cottonwood does coppice well, so that's great!
Fuel shortage definitely confirms that a combustion device would be better as a secondary heat source...
If heatsinks/thermal mass are not sufficient for primary heat source, the only other non-combustion options I can think of are:
-geothermal, already mentioned, expensive
-Solar, either direct via vacuum panels, or photovoltaic as per:
https://permies.com/t/45425/passive-solar/Passive-house-PV-electricity-heating#364288 (still expensive though)
-heat-pump, not sure if this is even possible at such low temps, doubt it
One nice part of radiant heating from solar of either sort is it would allow you to heat a mass... and then put plants on it. Bottom heat for propagation, built right in!
Don't forget about summer cooling; I expect you're planning for shade cloth and hopefully earthtubes for cool air input?