Welcome to Permies, Garret!
First, a few background questions. How large is "large"? What is your climate and how warm do you want to keep your
greenhouse?
Is your sketch showing 12" diameter logs? How long would they be? Would the "V" hopper be parallel or perpendicular to the burn tunnel?
The hopper might work to deliver logs as long as they stay in the right size range, but I think there would be difficulty keeping the fire burning properly. The logs need to be sufficiently in the coal bed to be hot
enough for reliable combustion, but not so much that they smother parts of the coals. The standard J-tube does this automatically, with the ends of logs standing in the coals, leaving enough airspace for oxygen without making a big lump of tight coal. It is possible that it might work reliably, but it is untested and you would need to experiment before depending on it for heat.
What size of system are you contemplating? The largest common size is 8" diameter throughout; larger ones have been built, but are rare. A 12" system would be truly a monster, and might require different treatment... nobody really knows for sure.
By "burning long", are you contemplating several days between tending? That sounds pretty risky. If you have a really big greenhouse, a mishap not caught for a couple of days could be very expensive. Also, there is generally no reason to keep a
rocket mass heater burning continuously except perhaps in the very coldest weather. The design gives a big slug of heat in a relatively short, hot fire, and the heat is all trapped and released over hours or days depending on the system configuration. Your hopper would essentially be running flat out no matter the weather, and would either be too hot on milder days or too cold on colder days. The
RMH is not a woodstove and does not need to run continuously to heat its space. This is something a lot of new people don't grasp at first.