"It would be difficult to run a shore cable without having to go outside."
If you can run 120 wire from the inverter to the ATS and from the ATS to the AC panel, why can't you instead just run 120 wire from the inverter to near the panel only with a receptacle on it instead of the ATS, and also since the shore power cord is on the AC panel, and you intend to run 120 wire from that panel to the ATS, then why can't you just plug the panel into that inverter receptacle, all inside the RV?
How will you run 120 wire from the Main breaker to the ATS as well as having the shore power cord on the Main breaker? However you do that, it should be the same as running 120 wire over to the inverter receptacle for manual plug in?
Sorry if I got the picture wrong, but it is interesting. Perhaps using an ATS for the inverter is something I could do too where my own set-up is kind of awkward.