I have been researching for about 3 years on this.
Here is what looks to me like the best idea for earth banking heat.
self heating green house
Now a possible way to pull the heat down into the ground would be a solar collector used to generate air flow instead of heat. The window screen box collectors seem to be winning the efficiency here. The blower fan can still go on the inlet end but the system would then do something even without electricity. Especially useful for getting a bit of annualized geothermal in the summer season.
Now some other things to add to your thinking.
Why are the trees at floor level? If you go deeper with them then you have more height to work with inside the building. So if your floor isn't level and you build some raised walk ways the base of the tree can be deeper still letting you have more height to work with. You still need proper air flow to the roots so you can't completely cover it but would pallets holding compost heating 6 inches up off the lower ground let you mostly surround the tree with compost heating?
The walls outside. Many of the do it cheap green houses uses straw or hay bales around the perimeter outside as ground insulation. It will add to your snow removal problems and but might be worth considering.
As for being able to do tropical plants are you also looking at doing greenhouses within greenhouses? One of the commonly given rules of thumb is that you get roughly 1 zone for each greenhouse layer. You might be able to surround your banana with water barrels on the back side and put it in its own green house. For my thinking since the goal is earth banking I need to pull that air down somewhere so If I am pulling the hottest air in the greenhouse down inside a separate greenhouse I may be able to create a hotter climate still without losing much during the day and by getting the water storage warmer carry some of that heat through the night as well. If you are constantly during the day flowing the hottest air in the building down past the barrels stratification wouldn't matter as much. For night time use a simple waste gate that allows the airflow to bypass the inner green house would let you keep that heat in the inner green house.
What are you doing for summer ventilation if what you have shown isn't enough? The worst case rule of thumb for natural ventilation says it needs to be 1/3 of the square footage of the green house. It seems to vary between that and saying you need 20%(10 in 10 out).
Have you looked at maybe building a ridged foam board multifold door to cover the glazing inside?
How are you using your other paths in the building. Some of the stuff suggest doing vermiculture under them.