Why not something as simple as a dual zone automatic transfer switch.
e.g https://www.ebay.com/itm/GCQ2-63-2P-63A-Dual-Power-Automatic-Transfer-Switch-ATSE-Switch-CB-Class-Switch-/174427269392
Theoretical vs practical. Theoretical.... don't go there.
Practical. 35mm wire should be fine because....
a) your batteries will die long before you will heat up/melt the wires and
b) look inside the inverter. You will most likely find substantially less wire sizes than you think.
I have 48v Lifepo4 batteries with the brand Deutche Technologies. They have a KYHT branded BMS inside (see http://www.kyhtbms.com/goods/show-135.html). I have tried contacting local battery supplier and the BMS manufacturer but have no joy in getting a response.
Does anyone have any information...