Not apposed to a rain hat but I don't use one. If I carry/wear a hat its my ball cap type with sun shade side panels. That suits me for most all conditions here. However if I were looking at spending extended period in the rain as you are, I could definitely see the advantage of not wearing a hood and having a more breathable set up.
If I were to go that route, I would be looking at something dual purpose that wasn't a sweat house for use when the sun breaks out. Many that I have tried on seem to be a little on the heavy side and not so well vented.
Recently I have been admiring vented Tilley hats I just really like the look and fit. Its the firm brim I like. I don't care for the floppy jungle roll ups out there. Probably stick with what I got for now.
jimmyb