Use that formula for computing wire gauge requirements.....6AWG might be enuf.
? Consider just adding a wire to the 6AWG in parallel to achieve the desired voltage drop.
I would prefer to increase the wire size/connectors/terminal posts whatever, and correct the loss in the 12 volts running to the front panel. Use the panel for the 12 volts that power the lights through the new relays. I would want to be getting maximum 12 volts to everything being powered.
You aren't having problems with the formulas and logic for computing the wire size are you. I think that is probably simple for you but I can't be sure. I will run the numbers for you if need be.