In case anyone is interested, the manual for Phoenix 12/375 (and other smaller Phoenix inverters) lists the following:
Low battery shut down (adjustable) 9,3 VDC
Low battery restart & alarm (adjustable) 10,9 VDC
Battery charged detect (adjustable) 14,0
I called Battle Born to ask as this didn't seem right for the LiFePO4 battery, and this is what they told me:
Low battery shut down (adjustable) 11-11.5 VDC
Low battery restart & alarm (adjustable) 0.5V higher than shut down - 11.5-12 VDC
Battery charged detect (adjustable) 13.2 VDC
I've set up my inverter like this, will see how it goes over the next 5 days out camping.
Hope this helps.