A 4" diameter system is very small for a
rocket mass heater, which is what you are making even if the primary purpose is cooking.
Heaters this small require everything to be done just right if they are to work at all, and even then it will not put out a lot of heat. I think you would be much better served by building a 6" diameter system, which is the smaller of the two standard sizes and is likely to work as long as you basically do things right. A 6"
RMH can support about 35' of horizontal duct run in the mass, minus 5' for every 90 degree bend. So an in & back run would have a maximum length of 25', or about 10' in, 5' at the end, and 10' back. If you want to exit at the far side, you could have 5' in, a 90 to run the length of the floor with 10 or 15' run, a 90 and 5' of run to the far wall and up. The duct in the floor will probably make a 2' wide strip somewhat warm, but will not affect the floor beyond that. 4" ducts are too small to carry the exhaust, and larger ducts would require a thicker bed of mass.
Sand is not a good mass material, as the tiny airspaces give it insulating properties. Mixing it with just
enough clay to make it solid will give a good thermal mass.
I think you might get better results by making a 10' long
cob bench on the inside with the duct doubling back inside it. This will give a positive warm place to sit, lie, sleep, and radiate some heat to the rest of the space. All of the mass will get warm and be beneficial instead of only a 2' strip of a whole floor.
Lastly, if you are really planning on living in this and heating with the
RMH, having the fire where you can't see or hear it without going outside will make it much trickier to tend the fire and keep it going steadily. About half of the heat from a standard RMH is radiated from the barrel, and you will get only the slow mass heat on the inside.
You might be best off building a standard RMH inside, and a
rocket stove outside. This would not preclude cooking soup etc. on top of the inside barrel. It is possible to build an effective rocket stove with cooktop entirely from cob (except for the steel plate and the chimney pipe), so it does not need to be expensive to make two systems, considering that they are not intended to last decades but just a few seasons hopefully while you build your house. If you want an example, I have posted pictures of a
cob rocket stove I built.