Might be time instead to pair a set of Honda EU2000i's for the full 4000 watts at start, and see if that resolves the problem. Seems like you are running out of amps for some reason.
He isn't having the issue at start up...
Where would you rank these brands in terms of quality?
Middle of the road. I don't believe there is such a thing a a high quality, mass produced toy hauler or RV for that matter. Those two terms are mutually exclusive.
I understand your feelings, but certainly one or more brands have to shine next to their competitors. Right?
No, not really. Why would you think that?
one might be better at one thing while the other sells on something different.