S.H.
Hi S.,
I learned this trick from ex-Mother-in-law whose husband had really bad ring around the collar. She used a "bad" shampoo such as Pert or Prell on the collar, did a little scrubbing and then dropped it in the wash. She said that because these shampoos strip the hair of its oil, it does the same for oil based stains such as the oil from perspiration. I've used it a few times and it works, you might want to try too.
As for the sweating itself, Certain Dri is a great 'prescription strengh' anti-perspirant and deoderant combo. I used it for awhile, but the anti-perspirant portion ended up irritating my skin. I have a friend who uses it and loves it though.