How about buying a breathable cap that you like and goving the bill a triple dose of DWR treatment? There are all kinds of cheap mesh trucker's caps. A mesh runner's cap or a sun hat like the OR Sun Runner could do double duty I fair weather.
Perhaps a silnylon sheath could be made for the bill, or even the bill and front panel?
I like idea. Many a bad hood has been fixed with a baseball cap. The bill would keep the spray off you face and glasses.