Without even a drillpress you're going to struggle building a back whether rotating or not. However...

The Toyo back design is made of folded metal so would be hard to directly replicate but the idea is not. Consider the back to be a square wooden thing which rests in a square recess on the rear standard of the camera. You can put the back in in any of 4 orientations and it will sit in exactly the right place as long as something is clamping it in. Toyos use sliding metal latches similar to the ones that typically hold a lensboard onto the front standard. Steve's idea of using magnets to retain the back is excellent though, especially if the non-magnet side was constructed from a 1.5mm sheet of mild steel.

See this photo. While it's the front of the camera, you can see the sliding bit of metal at the top that retains the lensboard - that's how the backs are often clamped in. Think of the back as being like the lensboard - square thing in square hole and clamped in somehow, though of course the back protrudes from its "hole" a lot further so that you can get film holders in. That's all you need to do.