I do a fair amount of camping at elevation, and you lose power as you go up and it's evident when trying to do things like start an a/c.
If you are going to spend the money on a 3KW inverter it would better to buy 2 EU2000is with a parallel kit for ± the same cost. You end up with more continuous power, more surge power, a lighter overall weight and easier to carry generators. You also can only take one if you don't need the a/c.
Either way you will need to re-jet the carb's, which is much easier on a EU2000is than a EU3000, but both can be done sitting on the tailgate.
I have a friend with a Yamaha 2400 and it will run his a/c at lower elevation.
Even with the parallel 2K's or a 3K I would put a hard start capacitor on the a/c, it really helps the startup. Supco SPP6E is a good model and they are well priced.
EDIT: I missed page 2 where you bought a EU2000, good call. I have the pair of Honda 2K's and my dad has the 3K, after a few weekends of camping he wants the 2K's.. an all around better package.