We actually did something similar but we used the heavy guage plastic under the tent. I think it was called 6ml guage. And we bought enough that we could double it over so basically it was that much heavier.
Another thing we always did when we picked a lot at the campgorund was we walked the site looking for glass shards, twigs, branches, stones and other sharp debris. If we really liked the site, we removed the stuff we thought would damage the floor but if there was too much junk, we looked for a cleaner lot.