13,
Does the inverter have a rocker switch?
If so, it is a pretty easy modification.
The type with a membrane push button switch are not so straight forward.
I believe inverter LVDs are intended to protect the inverter, not the battery.
That often works out well for me when I am trying to operate something with a long startup surge, and using undersize jumper cables between the battery and inverter. If the inverter went LVD at 12.2V or 11.9V, then it wouldn't get the power tool started.
G-