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Two thoughts for you. (1) If you are worried about the gearing, then by all means swap out the 26 chainring for a 24 or the cogset for a wider range. If you hit a tough grade that feels like it is going to wipe you out, it will be mentally tougher to get up it if you're thinking "why didn't I get lower gears when I had the chance." And if you don't need that new lowest gear, think what a morale booster that will be.
(2) As for washing clothes on tour, whether you do that in the shower or in a sink, consider getting a dunk bag. This is actually just a plain mesh bag (it can be made out of anything that can stand getting wet). Take your newly laundered jersey, shirt, shorts, whatever, put it/them in the bag, and twirl the thing like crazy over your head. The idea is to do your very own human-powered spin cycle. (Don't do this inside, though - it's kind of rude to splatter everything with water and you might hit something.) It works for cooking/eating stuff, too, as long as the stuff isn't breakable or sharp. The bag should about half again as big as you need to hold whatever you put in it to dry to allow you a good grip around the bag closure - don't depend on a draw-cord to have enough strength or grip in your hand for the job. That means you can get away with a smaller bag if you are willing to "spin cycle" each article of clothing separately than if you anticipate doing them together.
I do have a question for you, though. Does your weight budget have a line item for bike tools? Are you prepared to do repairs on the road? I don't mean servicing a bottom bracket or a repacking a hub (does anyone do that anymore?). But are you carrying tools to permit you to replace a busted spoke, or remove and reinstall your chain? I assume you will have tubes, patch kit and pump, but be sure to think through what other tools you should have as well. Having a breakdown on the road sucks. Having a breakdown on the road that you can't fix on the road sucks a lot worse, especially if it is one that could have been fixed on the road if you had thought to bring the right tool. This is the voice of unpleasant experience talking here - which may be why I'm the guy with two spare tubes, a patch kit, a spoke wrench, a chain breaker and an allen wrench set with me for even the shortest joy ride.