What happens when you remove the two jacks under the rear frame? Maybe even drop the tongue and add some weight to the rear bumper. The frame is pretty flexible, I had to jack mine up quite a bit to meet the shell when I did our shell-off.
Even with only one section removed, I wouldn't be surprised if it gave you enough play to slide a piece of plywood in there. I would hesitate to apply any pressure to the top of the compartment door, since warping the door frame could prevent the gasket from getting a good seal ever again.