Any tips for painting in high humidity?
Latex paint takes about 24-36 hours to cure in normal/optimal (50%) humidity environments, and longer to dry if your humidity is higher. The easiest way to bring down household humidity in the summer is to leave your A/C cranked down. Your air conditioner will remove humidity from the air. 

First, ensure that any patching you do has dried thoroughly. Prime the day before you paint. Put a fan on it and make sure that you don't use the shower for about six to 12 hours after priming. 

Don't use the shower for at least 12 hours after you paint. Then keep the room ventilated (which might mean showering with the door open and a fan blowing drier air in), and keep your A/C turned down so that your relative humidity stays lower.