I was tarping over my H18 with the wings folded up and the mast down in my yard. The key was tilting up the tongue of the trailer so the flat part of the tarp between the folded up wings was also sloped toward the back of the boat to stop puddles.
As for your cat problem (shredding the tramp), one solution is to put up a garage and close the door. Another one would be to get rid of the cats (just proposing ideas, I am not a fan of cats).
I am not a fan of cats either. I am thinking of buying a hobie cover for it and cut out for the wings. It seems the easiest thing to do other than kill the cats.