I also sweat a lot and the best way I've found of dealing with the discomfort is a merino wool baselayer. And not just for sports: I will probably never buy another pair of cotton boxers or socks.

Cotton gets wet, then cold and clingy, which can exacerbate blisters (socks). All sorts of high-tech synthetics start to stink real fast (I don't have much experience with silver-treated fabrics though). Wool wicks very well, will not stink even after a week of wear, it retains 50% heat insulation and does not cling against the body even if it is saturated with sweat + merino wool is too fine to be itchy and it stretches back for longer than most fabrics so cuffs etc can stay tight for years. They used to have wool jerseys at the Tour de France up to the 1980's since it beat synthetics for cooling up to that point. Couple of downsides though: merino wool (Ibex, Icebreaker etc) is expensive (but hard wearing), needs delicate detergents and does not like aggressive machine drying.

Bottom line: hundreds of millions of years of evolution for keeping warm-blooded animals performing from desert to arctic conditions has not been wasted.