Thank you everyone for the ideas. I'll be looking into them this week when life slows down a bit. I'll try to post pics of before and after.

Why does the PSP bag need to be waterproof?

Surely all the contents are unaffected by being wet or they would be ineligible for inclusion in a PSP in the first place.

Marine stores carry watertight bags with sealing rolltops for handheld radios which take the complete radio, aerial included and also ensure the radio floats. Like the Aquapac:

http://store.aquapac.net/explore-product-range/handheld-vhf-radio-cases.html