One thing I've thought about is modifying automated egg-turners. These are devices that sit inside an incubator and rock the eggs back and forth. Most have some adjustment of timing possible, and most will rock to one side a bit, wait a little, rock to the other side, wait a little, and repeat. They're very inexpensive.
The problem as I see it is that the whole tray doesn't rock, just individual rows, but perhaps that would be part of the modification process.