Not Hondas but I have two Champion 3100s that I can run in parallel providing 50A service and can pretty much run whatever I want. Have fully tested it with both A/Cs running.
I've also fully tested running just one inverter, and can start/run either A/C - but not both. A/Cs are 15k and 13.5k BTUs. With one inverter and A/C you're not going to be able to run much else.
The question you need to ask yourself is "how good do you want to feel?" My take was "pay once, cry once". That's why I went with the parallel setup. The Champion setup gives me 50A vs. 30A that the Honda gives you.