Did a vertical TLUD that ran a little better than 2kw for 13 hours some years back. The fill and burn chamber were less than 3 feet tall. Stack added another 3 feet. Have built many 2kw TLUDs that burn smoke for 8 hours for friends. Have also done horizontal pyrolysis using TLUD concepts.
In your case, for extended run time, an angled TLUD may be the ticket. Have yet to do one but been thinking bout it ;~)
In most TLUD designs, when the smoke burning stops, the char burning begins. Which means extended heat output at much lower rate (in my experience char kept burning for two days and char remained.)
Perfect combustion is what we seek. Creates carbon dioxide and water. Both great for plants. Plants return oxygen in the bargain.
That said, moisture buildup in an enclosed greenhouse can be problematic, promoting fungus and etc.
Check into thermosiphon for moving water through the greenhouse for heat where you need it. Simpler than it sounds. Best system I have personally seen to date is open at highest point so no accidental boiler.
An angled TLUD operating in batch mode could meet your spec with a reasonably standard fuel and careful design. Using water for heat storage and getting the temps into desired locations makes sense.
Moisture will likely be the "gotcha" running unvented. There are heat recovery ventilators that run off a humidistat to control humidity in the space, but then you are talking electricity.
With a large enough expansion chamber and rapid enough cooling from the water you could exhaust through a tiny pipe near the floor and maintain draft. But water exiting could freeze during extended low temps. A known issue with HRV's.
It makes sense to save char - make useful downstream product while heating.
Cheers and best wishes. Grow baby grow!