I have the same problem...I sweat buckets and buckets no matter what the season is, though it's definitely worse in the summer. My beam routines are magically better once it gets colder out because my feet are so much less slippery! I'll chalk them up before I go, but if it's warm out, they're soaked again by the middle of my routine. For me, I think it's genetic - my mother is even worse than I am. She's an ice skater, so it's always cold when she's working out, but she still gets giant sweat stains...
In practice I'd wear a sleeveless leo. It's much better for "airing." If you want, you could bring a rag or a towel to practice and slyly take it to the bathroom with you to wipe off your pits - cause teammates might think that's gross even though it works pretty well.
For comps, I'd advise you just to ignore it. If whomever cares more about your underarms than your skills, that's their problem. Anyway, don't teams all have to wear the same leos? Our comps are Sept - March so we usually don't have to deal with superhot temperatures. If you get pictures of yourself with stains...maybe you can digitally edit them.
