When I've smelt my worst on trail, the problem hasn't been a lack of water. (I do bring soap, a nylon bucket, and a piece of dollar-store chamois, and use them to bathe and wash socks.) It was because of an excess of water. When you've been hiking for days on a trail where the answer to, 'where's the next water?' is 'you're standing in it,' things start to reek, partly if not mostly of mildew (although beaver swamp water isn't very pleasant even when fresh). Stale DEET, and the Gurney Goo that I used to wax my feet, only added additional notes to the overall miasma. The peppermint scent of Dr Bronners was lost in the cloud.
After a trip in those conditions, my wife picked me up and we drove back to my car (rather a drive, it had been nearly a sixty-mile section, and the road took the long way round) with all the car windows open.
Despite the fact that it was snowing at the time.
And this was with bathing daily and washing a pair of socks every few hours. (I needed to do that anyway, to get the silt out of them, or they'd have rubbed my feet raw.)
Sometimes you just stink, and there's no help for it.
Fortunately, the AT isn't that wet in hiking season, even in Vermud.