It's so humid in central TX right now that I look like I went for a swim. I will wring out my gloves and skull cap at store stops and get half cup of sweat out of them.
No problems with slipping since I use the gel/cork HB tape and it has a decent grip to it.
I have a variety of LG, Specialized and PI gloves. They go in the wash after every ride. If not, they get very nasty.
I have no idea how to keep them dry through a long ride. I don't think it's possible.
The worst is when it's so humid you're shoes start to fill up with sweat!