Driving 12V signal from 5V pin

@HighSeraphim
Those circuits are unsuitable for delivering 12V, 5V and 0V to a pin, they are simply transistors driving a load to a fixed voltage.

I will also need a gate of some kind so that the shift registers in opposite directions don't screw each other up.

No you don't. All you need is an output enable line on the output shift register chip. This can be tied to the PROM output enable pin if it is the same way up or through an inverter if not.