Straton, I think I found a design that we'll both like.
When it's open, it will have a 1x4 under it like you wanted. While closing, it, the back will stick out a little (so it doesn't look like the cover suddenly shrinks), and the back brick that's sticking out will 'slide in' so it still looks like a 2x4 brick.
I'll update it at Badspot's server.