I have come to realise that stainless steel is quite a poor conductor of heat compared to other metals:-
I put a thermocouple in the heater and adjusted the power to get 240°C inside the brass part of the barrel. That only required 7.3W. I put another thermocouple at the top of the stainless steel barrel and that only reached 50°C.
Although this is just a lash up, it looks really promising. I can get the temperature even lower by using a CPU heatsink or a small fan. I will make a nozzle out of aluminium or copper with a built in heater and thermistor.
Not only will this stand temperatures up to the limit of the thermistor, which is 300C, but it is also much more rigid and does not change in length significantly with temperature. It should also reduce the amount of molten plastic because of the thermal gradient down the SS barrel. That should give less extruder overrun.