I live in Mobile, AL and we share rainstorms. Just bought a 40 year old house that looks like it was remodled by someone who knew how to use tools, but didnt know how to use them to remodel a house preoperly. I have more work cut out for me undoing stuff that's wrong and caused water damage than I have time for really.
But I know that here on the swamp coasts where we live, anual rainfall rivals the likes of Seattle, so moisture is a formidable enemy for wood even on the short-term.
I feel like air space that allows for flow is your best bet, so if you can just get sheets of anything up there at the rafters and sealed it would go a long way to cutting the noise. Maybe check at cabinet shops for scrap 1/4 inch luon. Its thin plywood sheets that cost $16 for for the full 96x48, but cabinet shops ought to have a good deal of scrap piled up and willing to let go for much cheaper per square foot. If I were to find enough scrap for the whole ceiling, it would look absurdly patch-work. I would probalby want to seal all the seams and then try to apply a clear coat or paint coat perhaps.