Ray, I'd take this a step further, possibly, and consider using a translucent LCD instead of the physical overlay film. They do exist affordably in the size you'd use for a Vectrex. You'd have not only the ability to have many overlays without swapping anything but you'd also have the ability for LIVE overlays.
I don't know the voltage ranges on the Vec for X and Y, but IIRC it's +12 to -12 for the WG vectors. Since you're working on an XY grid, presumably, in order to flip that X image you'd have to mathematically negate that value (multiply by -1).
I'm not sure how I would try that electrically as I'm not yet at the design capable stage of knowledge. I do know, though, that it would be simple if you were doing it in software. If you're going to use the straight Vec, you'd have to do it in hardware unless you wanted to produce an altered cart for each game. If you're going to emulate the Vec, and had the source code for the emulator, you could do it right there in a couple lines of code, or alternately in the ZVG itself if you had or could get the necessary source.
It could be a very simple thing to do, though, since either electrically or logically it is a simple operation. The next step here would be to make some design decisions and from there the best method will probably become clear.
I like the concept quite a bit. Keep going!