It's too early to make any real claims, but i did do a little initial testing of an idea for reducing odor in a non treated synthetic. Some background. Recently bought a few yards of polartec powerdry high efficiency baselayer fabric off ebay, and have been making various garments with it. A sleeveless shirt, a balaclava, a pair of mittens, and in the near future arm sleeves (i like adaptable/modular systems).
Since i was fairly sure it was untreated stuff as far as odor goes, thought about some easy, DIY ways to reduce same. Came back to Borax, one of my favorite "natural" cleaners that i use in various ways. I've noted that it has really awesome antimicrobial properties, while being fairly non toxic.
So decided to make a solution of borax in hot water (a few heaping tablespoons or so worth) and add it to the rinse cycle to leave bit of a residue in the PPDHE clothes i had made.
Recently went on a two day, one night trip. While it was a fairly easy and short trip, i did sweat a decent amount in the sleeveless shirt referenced above, and wore it the two days and a night. At the end of the trip, the arm pit area was a wee bit stinky, but pretty minimal all in all. The rest of the shirt had no noticeable odor (had wife confirm), even in the part of the shirt that goes over the small of the back where i tend to sweat a lot because of a pack.
Anyways, obviously if this works at all, it's only going to be a real temporary solution and probably only applicable to really short trips like the above, especially with less sweat involved.
Maybe others could experiment with it. I would recommend making a weak solution and testing it on your skin first to see if your skin will be ok with it. While fairly non toxic all in all, different people react differently to things, and it does have a high ph (as my well water is somewhat acidic, helps to offset this a bit). As i've previously used some in baths, and in our hot tub, i knew my skin was ok with even moderate solutions.

