Bring more dishes and utensils, and wash more dishes at a time, but less frequently. You will need space for them, but dishes and silverware pack up pretty easily anyway.
Most water waste is from washing few dishes at a time. With more dishes, and doing many dishes at once, and make the most of whatever improved method for washing you utilize. Leave a tub of water with diluted bleach or dish soap to soak the dishes you're saving up to have cleaned, so that food doesn't cling to the surface. Doing all the dishes at once will help you avoid that lame squirt-the-dish-soap-quick-wipe-clean that people usually do with their camping utensils. That wastes water, soap, and doesn't clean as well.
For your improved method of washing,
use this methodology. The key is boiling some hot water, get some real detergent, and do a proper cleaning.
Hot water. Not warmed water. Get some gloves if it's uncomfortable. It's gotta be
hot. Heat is what does the cleaning. Plus, washing dishes doesn't seem as gross and shitty with hot water. Let the sun do the drying to save yourself some extra work.
For keeping dishes sanitized, you can get some surface sanitizer such as
Star San. Star San A 1oz squeeze creates 5 gallons worth of sanitizing solution. Keep it in a bucket and you can use that all week long. An alternative is to put it in a squirt bottle. The sanitizer puts a tasteless acidic "film" on the dishes that prevents anything from growing on them. As you can see above, it's used in beermaking where keeping things sterile is very important.
Remember that you need to wash dishes in real detergent before using the sanitizer. The sanitizer alone is not enough to clean dishes, but prevents clean dishes from becoming contaminated.
