Nathan, if I were building a rocket stove for this space I would build a bell along the north wall of the greenhouse and use the top of the bell as a place for more plants.
The energy in wood derived solid fuel is mostly proportional to its density,so if you are planning to burn cardboard I would go for a very large j-tube or batch box rocket stove that can fit a lot in at one time.
This 8 inch J-tube that Uncle Mud could be ideal.
It has 6 whole barrels end to end as as a bell, and the area above the riser is insulated, so most of the heat is directed into the bell, instead of radiating out the tops and sides of the barrel.
They built theirs outside, and covered it with a hugel mound.
If you built yours indoors you could surround it with pallets so the sides were vertical,or just put pallets along the north side, and let the south side be sloped.
A 6 barrel bench is about 18 feet long.
Sizing the j tube up to 10 or even 12" could enable an even longer bench.
If the goal is to heat aquaponics water without changing the chemistry, stainless steel coils should do the trick.
If you station the sump tank above a heated bench, a homemade heat pipe could move the heat from the bench to the water.
Heat pipe video:
Check out this video, "diy heat pipe"