If your problem comes from sweat, you might want to try putting antiperspirant on your feet starting several days before the trip. I have heard of marathoners doing this. Glide reportedly helps deal with constantly wet feet also.

If the problem is outside moisture, look for footware that dries really quickly. Solomon and several other makers have their trail runner shoe without padding, just mesh, for water use. You might want to try these with a thin synthetic sock.
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If I wouldn't eat it at home, why would I want to eat it on the trail?