How do I prevent video interference caused by electric motors

David82:
the power supply isn't the problem from what my experiments have shown. Even when using batteries, the same action still causes the camera brown-out.

A brown-out indicates that the power supply (and regulator, and the circuit connecting all this to the load) isn't capable of supporting the load being placed on it. The fact that you see similar symptoms when running on batteries doesn't exonerate the power supply, it just means that you get the same problem running on batteries.