According to the commercials, AXE spray drives the women nuts.
I live in Arizona, and have a similar problem (heat, but not the humidity you have).
1. I ride easy IN to work. No need for me to try to get my workout GOING to work. I ride fast and hard going home, though.
2. I immediately go into the bathroom and sponge off with cool water.
3. I liberally use some deodorant.