I know you’ve stated your rabbits are pretty perfect with their litter habits, but even one pee which misses a box and gets on the furniture will seep in and potentially become a mold problem. With urine’s contents as well, it could begin chipping at paint or just find a single spot where the paint has an airbubble and seep through there. With large furniture DIYs, it’s not as easy to move it to peek around, checking for leaks or urine spots. Anywhere where the floor meets a wall, I would seal it or make the flooring material you choose run up the the walls partially to catch any urine.
For the backing, I’m tempted to say something solid. I like to think of hutches as some place a rabbit feels safe in if needed to be left there, and generally, solid walls with one/two-windows is safe for a rabbit, because their behinds feel secure while they can still see what’s going on. Wick outgrew his hutch majorly , but he loves it because it’s his “system of tunnels” in a way, with solid backing and open wire front. It’s his home-base that he doesn’t spend a lot of time in, but compulsively needs to check that it’s okay, and I think a lot of it is because he feels very safe in there.
I recommend putting panes or something along the bottom to a few inches up on the open wire side, so that hay, pee, poo, etc., can’t fall onto the floor from the top component. My initial thought is acrylic panes attached via zip ties.
If you do need to keep your rabbits there for an amount of time, the easiest way is install a latch on the bottom doors, or better yet get 2 dowel rod brackets (http://creativehouseblog.com/wp-content/uploads/2014/10/Photo-Aug-18-2-36-27-PM.jpg) and slide a dowel rod in. The latter is a bit better because with one latch in the middle, your rabbits still have some hinge-leeway when pushing on the door. With a dowel rod in place via two brackets across the length of both doors, neither doors will move.
A pull down blind installment on the front for the open mesh may not be a bad option as well, just in case circumstances require you need to cover up that mesh for any reason.
Adding a mid-shelf/ves would be fine in my opinion. If you’re worried about height restrictions, you can do just one over half the air space of the top component.
The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.