I tried the bed sheet tarp with limited success:
Tarp from a King bed sheet
I got hung up on the SilNylon treatment, and we settled in on the problem being a mix of low thread-count and 60/40 cotton/poly.
I'm looking at doing a diamond tarp from a tablecloth. Since these are crinkle taffeta (100% nylon a.f.a.i.k.) and have a dense weave, they should resolve both problems in one shot.
I think it should work something like this:
I'm going to mock one up in construction plastic before I order the tablecloth, to see what the coverage is going to be like but I think this is a go unless someone sees a problem......