That's a fine idea, bhchdh. I just grabbed one of those food storage bags with a plastic sliding closure, closed it and submerged it in a sink for a couple minutes. After removing it from the water, the inside of the bag was bone-dry. I put my phone it it and put it in my current case. It fit fine, and I could still hear it ring. I think I'll just start carrying the storage bag with me in case of bad weather.

Thanks very much. That'll save some cash. For some reason I never think of the home-grown solutions.