closed cell polyethylene foam...the packing stuff....you can get it in rolls up to 5' wide and 1/2" thick...fairly light material.....
over or under the roof....it wont absorb water either way and rolled up it stows easily...even 1/4" will deaden most "noise" from the agua
it cuts easily and adheres pretty good with contact cement spray
but....you already have this antagonistic relationship built up with "rain"....you must deal with that first...no insulation or sound deadener will help you....you'll just look for the noise and find it....
I too love the "noise" and sleep exceptionally well with the sound