Call Apple and ask to be transferred to "Customer Relations." Calmly explain the situation with them and give them all the case numbers you have so far. They may take care of you. ;)
Interestingly, when I encountered a problem today with my iPhone 4s being "water damaged" at the Genius Bar and I said the same thing about the only moisture it coming in contact with was from sweat while working out, I was told that it would take a lot more than just sweat to trigger the sensors. One guy used the word "submerged." The supervisor at Apple Care said that he had never heard of anyone claiming sweat as a possibility and therefore revoked my warranty.
Everyone agreed that using an iPhone and its apps for workouts was well within normal use so they "suggested" that there must have been some other exposure to liquid that caused the issue. But it hasn't ever been exposed to any other "liquid" than my sweat.
I find it funny that I've been able to find many instances like yours online about the sensors being tripped from normal workout use. I said that if sweat from having the phone in my pocket while using one of their exercise apps caused it, there must be a design flaw. The Apple Care supervisor vehemently denied it. I'm not thrilled about having had to pony up $199 for a replacement. This very well might be my last iPhone.