I use a MH1210A and the differential on that is 0.1úC where with the STC-1000 the differential is 0.3úC. But as said once at heat you don't need that much power. To reduce power there are two ways, either switch on and off or reduce the power, to reduce power again two ways, one is a big resistor in practical terms something like an old convector heater, or a transformer.
What I can say is in the Falklands our batteries were not lasting long and I decided what I needed was distilled water, belco boilers were easy to get hold of, but the output was too much to be able to cool with a simple length of pipe. So I tried powering from 110 volt, we had a large transformer so load was not a problem. I found it simmered nicely and although slow I was producing more distilled water than I needed.
So forgetting about transformers as likely you don't have one to hand, a convector heater same size as boiler is next best thing. I would use two controllers, controller one set at a lower than required temperature feed direct to boiler, controller two set at required temperature and it supplies the convector heater and the neutral of the convector heater is connected to line of boiler so they are in series. So controller one will give you the rapid heat up and controller two will keep the temperature steady.
copper is better than SS as its 40x 'better' at conducting heat (its coeficient of heat transfer is 40x bigger ..) 
