There are two wires only connected so you can't do a direct replacement. Likely you would need to fit the receiver with the time switch/programmer. But not simple change. So question is have you got the expertise required? There are hundreds of methods to control a house and I would suggest your not going to get the best using just a forum.
Wood burners to work efficiently need to run within a very narrow band. Too hot heat is wasted and too cold particular emissions and tar build up problems. So transferring heat into a heat store likely one way to be able to use rather than waste heat. Very few wood burners run efficiently most want the ambulance more than anything else. But wood prices will raise and maybe looking at efficiency now rather than latter is way forward.
Systems can be installed to use many heating sources all tied together
the picture shown likely not exactly what you want but just shows how they can be all connected together.
If you consider something like that to be long term gaol then using TRV will be moving in that direction. Whole idea is you pump hot water around the system if a room needs heat the valve is open so water goes through radiator if not then when all radiators valves are closed the relief valve will open and hot water is returned. The modern boiler has a system where the return water temperature is measured and the anti-cycle software decides how long to wait until the pump is restarted.
Putting thermostats in the rooms is rather an old method. Although there are now some really clever systems connected to the TRV which feed into a mini-computer.
But in your case the TRV seems likely the best way forward.
Also found this diagram for wood stove.
Nearly the same with few small changes and this is why I would say not really a DIY job but all examples seem to use TRV to control each room.
