My mini-split uses around 400 watts when it is on and it is several years old and not a particularly energy efficient model, so running a newer more efficient model is no problem.
As far as an incinerating toilet, I can't comment on that specifically, but I could recommend a maceration sewage pump which would allow you to move the waste practically anywhere you wanted for storage, disposal, or even incineration. I have been using one of these for a couple of years with no problems.
Just out of curiosity, why is a septic system not an option? There may be other similar systems that would work.