Brandon, you could also do a bell, it holds heat for less time, but it's lighter. Tho, depending on the insulative properties of the bell material, you can regulate the speed at which the heat is released and the heat accumulation.
For example, cob will release heat slower than concrete, and concrete slower than metal. You can also do single bell, or double bell. (the barrel is somewhat a bell in certain conditions)
IIRC concrete will hold more heat than cob for the same thickness.
You could also check the half barrel system.
http://donkey32.proboards.com/index.cgi?board=experiment&action=display&thread=560 It's another type of horizontal bell. Onto which you can put some mass.
The advantage of the bell is that heated gasses stay trapped on top. And the exhaust of the bell is on the bottom. Ok, they get diluted if you don't block the feed tube, but if you do, via movements of convection, the top stays hotter.
Besides that, i don't know about the states, but in France, where i live, a wooden floor has to resist to 300kg per square meter permanently. That provides with a bit or leaway for mass. Tho, not huge ammounts.