Most plastic tanks sold now have been tested with a 500 hour boil test BS4213:2004. Boiling water will never exceed 100 degrees in 1 atmosphere of pressure, to go higher in temperature you have to pressurise it. Yes, a copper overflow pipe will be needed and a copper float (if your float is not certified as boil proof), the Solid Fuel Association nor Doc J does not state that you have to have a copper, galvanised or stainless steel F&E tank with solid fuel.
Bear in mind that for a 350litre thermal store and solid fuel, you will need 10% expansion vollume. So you system volume could be around 600 litres, so you will need at least a 70 litre F&E.
Sizing the boiler, if a new build 50W/m2, renovated older house, with good insulation then 75w/m2, if old and solid walls but double glazing and loft insulation then 100W/m2. If un renovated, high ceilings, single glaze, poor insulation and drafty, then 125 to 150w/m2. You unfloor heating maximum is usuallly around 100w/m2 max with tiles. To get more out, you will probably exceed the maximum legal floor temperature.
On top of the heating load, as a rule of thumb, I would add around 0.5kW/person. 4 people = 2kW, 6 people = 3kW hot water load. So I think you need to keep with a 32kW capable boiler. I would size with the wood boiler unless you are sure that this will suppliment the oil boiler. It probably won't be lit at 7am in the morning when the house needs to be heated up.
You will still need a suitably sized gravity fed heat leak radiator with the 350 Thermal store. It should be connected via 28mm pipe most of the way and configured with the flow at the high port of the rad and the return at the low siide, a normally open two port valve, so if the thermal store is full of heat or the power fails it cuts in the heat leak. Diagrams and wiring are in the instructions with the Torrent. Better still, you should install the wood boiler with a flue thermosat, a laddomat valve/pump with a 65 degree return load/layering valve bult in, this will only switch the pump on when you have lit the stove and prevent the condensing / rapid corosion of the wood boiler, which you will have a big problem with condensation when trying to heat a large capacity system and a 350 litre store.
The other way to have a small boiler is have a very large accumulator/thermal store. It would need to be around 2000-3000 litres to start to spread the load so you could use a 20kW boiler, so the smaller oil boiler could run for longer to spread the load, the tank would smooth over peaks and troughs in load. Basically a crazy idea for oil, where kW's are cheap!!