If you've ever seen one of those dashboard beanbags that you can use for a GPS or cellphone..I think they're silly in general, but this might actually be a justifiable use situation. You can usually find them at radioshacks or department-store car or electronics sections..I want to say around $15-35. Stable, malleable, and heat resistant!
You might have to stuff something like a small doorjam or shim underneath the front or back to get your vertical keystone just right.
If projectors didn't get so hot I'd suggest trying to use the packing material it came with that held it still inside the box, but I'm afraid for what it might do to the styrofoam.