So I'd need to see a pic of your current stand, but it's doable. If you're handy enough with tools then you should be able to build a 6" platform the same height as your current stand. Attach the 2 closest legs of the platform to the old stand. Then lay a 2'x4' sheet of ~1/4" ply (1/2" would be better, but you do what you can with what you have). Screw it in, making sure you sink the screw heads below the level of the ply. Put your sheet of styrofoam and you're good to go.
btw, put some sort of brace between the legs of the platform or skin it w/ ply or something to make sure they don't bend the screws.