I think the official roof rack weight limit is around 30 lbs., so haul at your own risk...
The rails are wide enough that you probably can get away with not having cross bracing for the plywood sheets. For drywall, a few 1x3 pieces a couple inches wider than 4' should work, but know that the rack may not be as flat as the sheets, so you may want to shim the rear 1x3.
Not sure how you'd secure the bracing to the rack without making permanent holes- small clamps?
I would either use pallet wrap or lots of twine to tie the sheets to the roof.
Do you need a full 4x8 sheet or can you have the yard rip them to 2x8? That size will fit with the seats down.