From what I understand to run an air cond of an inverter you need a huge inverter and enough batterys with it , somthing to do with an inverter limited to about 150% of its rated load , but a generator will produce much more than that for long enough to start it, like a 2k inverter compards to a 2k generator .
I wish I was savy enough to post diagrams of things like this, and had a conection speed high enough to do it but Im old school , more hands on understanding
I live in Pleasant Valley 8 or 10 miles from you and it would take me less time to old school drive to your house , then to type with 2 fingers and download things to a site and post them .
I dont know why people would wire that way either
You also said you woulnt buy a newer Cub with the info provided , I would have no use for one either, maybe it would be a good fit with a on board onan gen ,I ripped mine out to use a honda
You for sure dont want to wire an inverter output to a breaker in a panel fed by shore power and just flip diffrent breakers on and off , it may work , but your one flip away from disaster, you need a inverter subpanel and to rewire the circuts you want feed to it . Then when the tranfer switch sences ac power it passes thru the inverter