Opinions are plentiful on this forum! :)
I would not bother just trying to barely make do with a too small generator. If you really need the AC, just get two small gens, or one larger one. While the Honda 2200 make work, when conditions are right, it is like towing with a barely capable too small truck.
Just a thought, but you can buy two similar sized generators, different brand, for the cost of one Honda 2200.
Jerry