Alternator hot Idle speed amperage can be poor. Mine is not very capable at all at Hot idle of ~550 rpm, at about 32 amps. At 800rpm this shoots up to 65amps.
As such I never Idle only to recharge.
Sounds like yours is not much better at Idle speeds and fatter wire might do nothing to improve idle speed amperage. But bulking up the OEM charging circuit can't hurt.
See if the jumper cables on Alt(+) studs to engine battery makes any difference in idle speed voltage held when under inverter/charger load to depleted house battery.