I think you will be unlucky, by virtue of the current @ 12V that would be required for the heater, let alone for the motor etc. Even a 1200 Watt machine would require 100 amps @12V- a tall order even for a bank of batteries.
I have a washing machine in my motor cruiser. It is a baby Bendix, operating on 240V, ie when you have shore power. Although I have a genny as well, it is highly unlikely I will ever operate it without shore power.
So I think a small mains version is you best bet.
Rgds
Stuart
I see you have found your way to a forum that will give you good advice. I have used the small pressure type. [Better than the bucket recommended on scuttlebutt.] Works OK for small loads, needs some hot water that can be heated on the stove. I have used another system which works well if you have time. Suspend with an elastic bungee cord a bucket with a sealed lid in say the shower or some such and sail about for a while, the jiggling and shaking will agitate and clean things up a treat. Saves on power and effort, but a little slow. Only other things I have seen use power inverters and lots of electricity, or else connect to shore power when alongside.
On reading your replies, I think the best thing you can do is - INSTALL A WOMAN.
Doubles as a dishwasher and electric blanket for the bunk too. Not to mention all the other amenities, Non of which draws power from your batteries.