Site selection is of course a great answer, but most of us know that in many places you are required to stay in very particular, and well impacted/compacted spots.
I like the tyvek idea myself, but as mentioned it can be exceptionally slippery. I've used a small piece of a poly-tarp myself as a landing mat under my hammock for years. It has grommets so I can tack it down in wind if needed, and it makes a nice sit pad on wet trails as well. You could cut a 5x7 piece fairly easily from a $5 box store poly tarp. 4 binder clips and a few folds and you'd have a bathroom floor setup.
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