240V split phase inverter

I know nothing about the brands, but if you google 240 v split phase inverter 12v you will find some.

Yes and no... My Xantrex Prosine 2.0 is a 2000 watt single phase 120 volt inverter. HOwever there is a jack on it, Standard modular Telephone type jack

Put two of 'em side by side.. Connect one of the output wires together, Plug in a cable to the two jacks, and you have exactly what you are asking about, a 240 volt Split phase inverter (120--120 240 volt end to end. Just like shore power.

They come in other sizes as well. Now the Prosine is no more (They discontinued) but I'm sure they have other models that work much the same.

Yes, we had one when I worked for the Navy... we used it and about a ton of batteries to power equipment when we had to make no (zero) mechanical noise
It was a Xantrek, but looking through their web-site I'm not finding the model

My Magnum 2812 has L1 and L2 in

Hi,

Yes it exists. Look at the Magnum inverter/chargers, or other high end makes such as Victron and Outback.

Probably not a big enough battery bank to supply all the power for 50 amp service.