What you envision has already been done, but for break-apart frames. If you go to the S&S website, you will see that the suitcase they sell is at exactly the airline limit size. The case is basically a square which JUST fits the wheels, exactly the same as what you envision in your diagram and explaination. It takes me half an hour of painstakingly stacking each wheel, frame, and component piece to get the bike inside the case. It's a jigsaw exercise that requires the left side crank and handlebar to be threaded through the spokes of the adjacently sitting wheel.

There is NO WAY a non-breaking 58cm bike will fit into a case that is airline legal. My advice: skip eating out for the next two months and buy an S&S coupling equipped bike. With the money you save on airline charges, you'll make the cost back in just a couple of round trips.