I am planning to make a board for mine this weekend - it appears to be simple. I'm planning to go to the local hobby shop and buy a sheet of 1/8" model airplane plywood. It's 6"x12". Saw it in half so you have two pieces 6" on a side. Cut down one piece to 5.5" square and glue the two together centered. Then cut the hole for the lens. I've done it for other cameras with hand tools, so I don't see why the Burke and James will be any more difficult.
Good luck.