We are looking at installing a thermal mass in our newly purchased house. We would like to install a rocket stove, but very much doubt we could get council approval, so are looking at running the chimney of a conventional woodstove though an adobe bench, or making a solar heater outside and running the heat through the bench during the day. we are not sure how heavy that adobe would be, though, and how much weight a raised chipboard floor can hold.
We plan to extend the house in the next 5-10 years, so don't want anything too expensive that can't be moved. Were also looking at making a cage of rocks or glass bottles filled with water with a bench on top, but again, don't know about the weight, or whether they would pick up much heat from the lower temperature of a solar heater. We are in new Zealand with an average range of 10C max and 5C min in mid-winter, but only 20C max in summer (you can use the fire in the middle of summer).
Running the flue of a conventional stove is not a good idea as the combustion does not always deal with the creosote, so you will have tar condensing in the flue when it is cold. There is a fairly recent topic here https://permies.com/t/12539/stoves/RMH-Suspended-Wood-Floor about building a rocket mass heater on a suspended floor. Floors in the UK often have a loading spec of 150lb/sqft, but with a large load of a few tons that a stove would normally have, extra support is probably needed. Moving a stove once it's built would be a bigger task than building it in the first place. You may as well stick with a steel box stove and stack some bricks round it, that's what I tried this winter and it does make the stove a more comfortable heat source..