I have a use-case for the AutoTransformer that is different from what I see generally discussed. I want to use it in my RV to take in 120v 60 Hz from either my Onan Generator (2 separate 120v legs that are SAME phase) or the shore power inlet (30/15 Amp which are 120v 60Hz single phase). I have those 2 inputs going to an automatic transfer switch so whichever one is "on" will pass through to the AutoTransformer. I would like for the AutoTransformer to step up the voltage from 120v single phase to 120v/240v split phase. I will then pass that split phase into the input side of my dual inverters (one inverter for each 120v leg) so that when I have a single leg input, I still get both inverters charging instead of one side passing through voltage and the other rejecting the phase and inverting to make the "correct" phase.
So, my question is, how should this be wired up to the inverter. It has labeled "input" and "output" sides but the "input" side only has 240v Line and Neutral labeled connectors. The "output" side has 120v Line 1, Neutral, 120v Line 2 connectors.
My intuition tells me to disregard the input/output labeling and connect my source 120v power with:
source 120v Line > AutoTransformer "output" Neutral
source Neutral > AutoTransformer "output" 120v Line 1
Then my output would be the 240v wave form stepped up via transformer as measured between the "input" Neutral and "input 240v Line connectors. I would need to carry over the neutral from the other side to provide 120v/240v split phase.
It is this last part I am unsure of and need some guidance on.
Diagram attached of my planned whole system that hopefully makes clear what I am trying to achieve.