You seem to have visited so briefly that you missed the fact that this is not a "travel" website but a "backcountry hiking" website. I'm no sure if our feedback is precisely what you are looking for, but fwiw:

I carry a USA-style washcloth when backpacking. I use it first for washing the dust and sweat off me at the end of the day (no soap!). Then I wring it out as much as I can and use it as a 'towel' to mop up as much water as possible. I've experimented with both cotton washcloths and the synthetic "cleaning cloths" that have a terrycloth-like texture. The cotton ones dry a bit more slowly and are a few grams heavier, but they do a better job overall, so I favor the cotton over the synthetics. For me, weight comes first, but all the factors you mentioned get considered as well.

FYI, I am perfectly happy with my current solution and no product you create would be cheap enough, as readily available, or more practical for my purposes than what I now use.