Another option to elimiate the leaks is to create a third box that would cover the others from the front. Thus creating a "triple box" not unlike the ones your film comes in. The only opportunities for leaks in this arraingment is from your lens openings (you would need two, one in each of the front panels) and from any faulty seams. This will also eliminate the need to re-seal the camera with tape everytime you load. It will be faster and last longer. I would also suggest using black silicon sealer on the interior seams of the panels instead of glue when you assemble the box. This stuff is amazing at sealing our light and will add a great deal of strength to the assembly. Use plenty during construction and you can trim off excess after it has cured.
While you are building, make your box a little oversized in one dimension to make it easier to "grab your film or paper by one edge during the unloading step. If you carve a shallow finger sized relief in the back panel, it will help you get behind the film when you unload. Also, glue some small strips of foam core or other inert and cheap (after all, this is the goal,yes?) to three walls of the "film back", ALMOST up against the back. Leave about a millimeter or so to allow the paper to fit behind them. Think of the "grooves" in a standard film back to get the idea. This will help hold the film/paper in place during transport and eliminate any need to tape it in place. If you choose to glue in these shims, remember to carve your "finger hole" near the wall that does not have a shim. Can't wait to see your images!