Rewiring battery bank to charger/inverter, couple of ?'s

When it comes to inverters, wire sizing is based on current handling AND voltage drop. #4 can handle 160 amps with 105C insulation but the voltage drop at that current level at 15 feet of wire is over 1V. At 45 amps it's only .3V but that's .3V less room you have before you hit the inverter low voltage alarm. I always follow the inverter manufacturers wiring instructions even if it's overkill. There's a reason they go to the trouble of doing that.