For the record Karl my experience with TLUD's and RMH's (which are similar to masonry stoves at least in the concept of storing thermal energy) is purely theoretical since I haven't yet built mine. That and I'm sure there are people on this forum who know more about it. I certainly don't mind speculating about it with you, I just wanted to be upfront so that you wouldn't mistake my conjecture/ideas for experiences and to encourage you to also seek out those with more experience and knowledge than myself. I really don't know anything about the setup of masonry stoves so I'm not sure how that set up would work.
I will answer your question with a question however! Wouldn't a cob type setup for the thermal mass be far cheaper than masonry stone? I am also a little confused as to where the secondary air comes into play in your system, and how easy/difficult it would be to change out the char/fuel. I think a better option might be a setup similar to that of the jolly roger, except the containers are surrounded (not on all sides) by the cob mix (and the appropriate fire retardation), and exhaust pipe is vented through more thermal mass on its way out of the green house. I would use something smaller than the 55 gal drums (as that setup is very large) maybe, and have it inside of the green house. I'm not sure how feasible it is to expect the exhaust gasses to travel through different changes of elevation, but I assume as long as the route isnt too complex and that it ends higher up than the unit (and outside in the colder air) that it should updraft okay? Maybe someone with more experience could chime in.
For the record I'm not bashing your masonry idea, I just have nill experience/knowledge of the units so you'll have ask around about that! I do very much like the idea of thermal mass heaters in green houses though, its one I've considered myself, and with the added bonus of burning manure and creating biochar, it seems win win, assuming it can be made to work