You also have the option of dual 2000 watt inverters, smaller, easier to handle, and can be paralleled to give a total of 3200-4000 watts, Generally one will not run an ac, 2 will run one and have some surplus for additional loads. Also there are 3000-3500 watt inverters from champion, predator, and others which are less than half the price of the Honda or Yammy's. Nobody will argue that the champs and others are quieter or longer lasting than the premium ones, but they do have a following and many will tell you that with the price point, they could afford to buy a new one every 4 years, and still come out ahead.
Lots of head scratching available on this one.
happy motorin