Might be able to laminate 3/4" plywood of a size such that it will fit between the cross beam ribs and goes wall to wall. Use a power plane and shape it to the underside roof profile, keeping it 1.5" thick minimum. Use sub-floor adhesive to glue it to the underside of the roof.
Another option would be to do a similar thing, but use thinner plywood and laminate in place.