Mine is an open center. I recently closed it up. The first time laying on the open center trying to work under the jeep was uncomfortable enough to make me finish out the center. It's so much nicer now. I also don't have to worry about my kiddos falling through the middle of the trailer now whenever they're up there playing while we're at camp.
What about putting expanded or grate down the center? It still is open to drips/cleaning but you can lay on it. You could have the panels remove/hinge to load spares or wood under the "deck".
I have a trailer that uses catwalk type grate for the deck. The trailer pulls like crap, but being able to tie small stuff down anywhere and crap falling through, keeps it around.