need to know thickness of a torsion box?

I have a torsion box that is 1' x 4'. The grid inside is 5 rows by 8 columns made of 3/4" plywood. The skin is two sheets of 1/2" plywood.

The assembly is firmly attached at both ends.

How thick would I have to make the overall box so that it would hold a 360 pound load in the center? How thick for about a 550 pound load in the center? And by "hold" I mean so that it doesn't bend more than about 1/4 to 3/4 inches.

would an overall height of 2.5" do it or would I need to bump that up to 4". I want it to be safe, but I am running out of room too, and looking for ways to reasonably reduce the height of it.