The inverter alarming at battery loaded voltage of 11.6 needs a look IMO. Inverters usually have 11v for alarm and 10.5v for shut- off.
So the inverter is maybe "seeing" 11v when batts are at 11.6. The 2/0 wiring is fat enough, so what about that buss/switch as the problem?
Two 6s can handle 100a inverter loads ok when batts are at higher SOCs, down to about 75% SOC, before loaded voltage hits 11v from what I have seen. ( YMMV, and 12s and AGMs do better from reports on here by others testing their set-ups)
Having four 6s lets you operate down to near 50% SOC before that 100a load will have them at 11v inverter alarm.
Once you are at the initial drop in voltage the voltage will taper while the load continues to run. So this is another reason to have a bigger battery bank.
Two 6s can do it at the higher SOC and for a more limited duration before hitting 11v. But they can do that--getting an alarm at 11.6 with a high SOC bank of two 6s is not right.