My favorite sun hat is the Sunday Afternoons Adventure hat. Yes, it's dorky, but it keeps the sun off, is well ventilated, and has a drape in the back so there's no brim sticking out to get into fights with my pack!
Also, I can pull my rain jacket hood over the hat; it squashes the brim in a bit at the sides but the hat brim gives me as good a cover as an umbrella over my glasses. The brim holds up to rain just fine. It's also a great base for a mosquito headnet!
You'll probably have to order it from REI or somewhere, so you may not get it in time for your trip. Consider it for future use, though. I use mine not only on the trail but at home for gardening!
Have a great time on on your trip!