Voltage boost from battery bank

Voltage boost from battery bank

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Hi,
I'm having some trouble with my inverter, and I'm hoping to find someone who has faced (and resolved) this sort of issue.
We live completely off-grid, and have a 650AH battery bank charged by 1KW of panels, and charge-controlled via two Tracer MPPT charge controllers. Overall, it works great. But recently, we added a third inverter; a 2kw/4kw peak pure sine, to run a refrigerator. Everything is fine while the sun in shining, and the charge controllers are keeping the voltage around 15v. The batteries are always fully charged by the middle of the day, and the charge controllers go into 'float' mode. Then, when the sun sets, the voltage in the system drops to the actual battery voltage of 12-14ish volts, and the largest inverter starts complaining of 'low voltage'. This is caused by the voltage drop induced by the additional draw (similar to when your lights dim because your refrigerator kicked on). When the voltage is about 15v, the drop caused by using the inverter is still within the constraints, but if the initial voltage is 14 or less, the voltage drop induced by using the inverter drags it low enough that the inverter shuts off with the 'low voltage' alarm blaring.
I have 4Ga wire everywhere, and the positive is connected at one end of the battery bank, and the negative is connected at the other. One charge controller is connected the same, and the other (along with the other inverters, used for running lights, occasional TV, and kitchen appliances) are connected the opposite. Everything is 12v.
I'd like to find a voltage step-up supply to bring the inverter input up to 15v or so, but I can't find anything able to handle the amps it draws. I've thought about upgrading me cable, but 4ga mathematically should be enough (in fact, the inverter only recommends 6ga.) This happens even with no other load to the system (i.e. with the other inverters and the DC stuff disconnected.)
I know the obvious answer is 'you should've spent more on your inverter', but since budget is a huge constraint, I need to find another fix for this.
Thanks!

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Voltage boost from battery bank