Danby makes a mini-washer set, agitator drum and separate 1600rpm spin dry drum that is rated for 10 pound loads; it is almost 100% manual operation and you can use the rinse water from one cycle to be the wash water from the next cycle if water is an issue. Some people love them, some hate them - you get almost no automatic cycles provided but nearly infinite control by tweaking stuff manually. One minus may be it does not like truly hot water, use only water under 50C. The specifications list maximum power draw is 120VAC is 480 watts, maximum wash water level uses 50 liters..

Remember it is from a small output product line so the price is pretty steep ($325~ shipped) compared to big-box store plain base models.

If you have a drier 240VAC appliance it really is the only option for full-size driers. Shorter run times and better mechanical efficiencies across the board IF you can even find a 120VAC heated drier.

http://www.danby.com/product/DTT420W/5

 You won't find a 120v a/c model that is more efficient, and most of them take real small loads and increase the drying time required!

 I have one I attached over my concrete sink, and it probably saves me 75% fuel and drying time. (I use a natural gas dryer) I got it off an old junk washing machine, which are pretty rare these days..

http://www.laundry-alternative.com/drying.htm

I normally spin clothes 'damp dry' then hang in closet, on plastic hangers to dry.

I think the extractor will be your best bet. Extractor, fan and dehumidified closet would probably dry quickly.