I wish I did, NutellaBear, but I'm hopeless with DIY stuff. That said, your plan sounds like it would work just fine. I looked back through some threads that I'd read before on building shelters using styrofoam, but I didn't see anything about how it could be weighed down.
There are some members here who've built some pretty impressive shelters, so maybe they'll be along with some ideas. I know builder is one of them - he's also made some pretty spectacular outdoor enclosures and such, so he might have some suggestions that would work.
If you haven't checked out the sticky on shelters on this forum, there are some links that might have some info too.