Jack, your last explanation clears it up, I approached polycryo with extreme skepticism, not believing that it could work, but it does. However, you are doing the one thing it cannot do: putting sharp heavy edges on it, like rocks on rocks.
With some creativity, you could get around that, like, getting cuben type 2 sided tape, and tape on reinforced tieout points on the corners that you then put rocks on, or something like that.
Cuben would work well too on the corners, taped, then you could sew on 4 tieout loops, or something.
The wondrous polycryo, which is just insanely tough for its weight, really does work... unless you do exactly what you do, sharp rocks on rock, then it will of course tear, it's not magic. That's by the way why cuben exists, to take that toughness but make it not tear, by putting in a mesh of dyneema between the tough plastic sheeting.
The dirt issue is easily resolved, you can either wash the sheet out in a stream and let it dry during lunch, or hose it off on a clothes drying rack when you get home, that works great, I do it after each trip, dirty brown water then it's clean, no need to wash beyond that rinse.
But rocks on it, with sharp edges, no, that most certainly will not work, unless you do more to reinforce and create tieouts. Which is not by the way hard to do..
Tyvek at around 5 oz for the ground cover is the way to go, it's tougher, not water proof at all, but it does resist water a bit, when I first ordered that I had to scratch my head, it totally did not fit with UL ideas, but it is durable and tough, just don't think of it as anything better than water resistant, even new I think it has a hydrostatic head of somethign around 600 off the top of my head, and that's the thick stuff they use at construction sites, or that zpacks sells. The thinner stuff you can literally see light through the holes, it has no hydrastatic head at all, it's the softer variant, sometimes used for kites etc. I want to say it's 1433 or something, could be wrong. So get the stuff from the constuction guys or from zpacks, that's what you want.
You can also add tieouts to that by the way, some how to do that on bpl, a few folds of the corners and then some other tricks I can't remember, maybe grommets, and there you are.
Good luck. For all other circumstances I've found so far though, polycryo works, something that never ceases to amaze me.