I think I remember that as well that trampolines seemed to be always wet when I wanted to use them.
Its either the plastic used for trampolines or that thousand tiny holes in that plastic.
What about cracking/breaking it on all 4 sides and making a little hole in the middle so you have kind of a funnel, all you need to do would be to put a glass below the hole each night.
you wont be able to jump around on it anymore tho
btw is it maybe possible to replace eg. the plastic only of a trampline that which you jump on? so we could build a funnel without destroying the precious trampoline.
Wilfried