That's what we are trying to figure out. If you tap into the generator feed to the existing ATS you might be fine with a single phase setup. The generator is single phase (I'm pretty sure) so the camper would just see the inverter as a generator. Just need to figure out the specifics of the genset and load management. Which is why @smoothJoey is asking all these questions.
Not sure if this helps at all, but I believe I have a similar system as the OP. I have an Onan Single Phase 120V generator, and my motorhome has an energy management system. When running on generator, my ATS sends the (1) leg from the generator to both halves of my 120v distribution panel. There are a series of relays that then will essentially prevent me from using too much while on the generator by opening and closing contacts, for example, in the 12v control wiring to my rooftop AC units, as well as the water heater. When on shore power, the energy management system “knows” and will allow me to run whatever I want.
When I do my system (I think I’m holding out for the MPii 24/3000/120 x 2) I think I am going to leave the energy management system in place (my generator will remain). I’m not sure yet how the energy management system will play with the new system, however, it does what it does based on whether or not it has 240v going to the panel (shore power) or 120v to both sides (generator)
Intellitec Model 900 Smart Energy Management System. Remove the fed front, under the bottom breaker is a circuit board that spans the width of the panel. Several lugs and relays on it that handle the load shedding.