It is not the "SOC voltage" that causes the shut down, it is the loaded voltage, which depends on the size of the load in amps wrt the wiring gauge/length and the battery R.
Keeping the SOC to some lower limit is only part of the story
It seems the BMS "sees" battery voltage as loaded depending on battery R while the inverter "sees" the loaded voltage with wiring R voltage drop too, so it will be a lower voltage. Meanwhile the battery monitor "sees" the (higher) battery loaded voltage.
You can't control battery R except by adding more AH to reduce bank R, but you can improve the wiring R part of voltage drop. You can control the size of the load by not using a big load when voltage is low (but you might want to!)
If you want to exploit the lower SOC with no harm operating range of the LFP, you will want to "over-do" the wiring to the inverter to keep that part of the voltage drop to a minimum, since the battery loaded voltage will be lower at a low SOC (not much lower with the "flat" voltage/SOC)
You have fixed shut-offs from drop-in LFP BMS, or ? tunable settings with BMSs for roll-your-own LFPs. You can have a shut-off setting with the battery monitor too (ISTR Victron has that?) And the inverter has a fixed shut off. Looks like you have to juggle all that somehow.
Without some kind of monitor you can't tell where you are at to operate it all. People don't want to do all that thinking while RVing, so somebody has to do the juggling ahead of time for their set-ups if they don't do it themselves so they can just go camping and no worries.
