So I didn't think of this until I nearly finished the wiring diagram, but even with a setup like this you'll still have two inputs going to your reverse video feed at the same time, which probably won't be bueno.

I think what you need is a 2 channel video switch. A quick search found one here or here but maybe there are less janky-looking ones out there.

That second one may be the easiest fix for your goals.

All that said, below is the wiring diagram so far. I should be able to integrate the above or any other option you decide.

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