MrMark:
You want to maximize the working range of voltage in the capacitor. Assuming this is set by the working range of your video module (7.4V to 24V), you want a capacitor and charging system that goes to 24V full charge. This allows the use of (24 - 7.4)/24 = 69% of the total capacity of the capacitor.
Except that even a 20V supercapacitor costs at least $13 and has a capacity of only 4.7mf.
As stated in post #1, I thought of using a boost converter to achieve 9v or 12v. I'm trying to find the optimal combination of voltage, capacity, and ESR for the supercapacitor, but don't know how to figure that out.