I'd buy a quieter Gen..........Bruce
Given the photo posted, he already HAS possibly the quietest generator on the market, so that doesn't seem probable.
I have seen quite noisy generators placed in open-topped boxes about 50 lined inside with 3" or 4" thick foam and the noise level (except almost directly ABOVE the unit) is incredibly quieter.
The box in reality only needs to be 4 sides, with no top OR bottom, and the sides can be carried as a stack, and assembled on-site for easy transport.
Just leave about a foot in all directions from the generator so it can "breathe" and get cooling air.
This works with most all modern 3600rpm generators that are moderately muffled to begin with, the final result being that they are almost as quiet as the inverter Hondas for a small fraction of the price. I have a Honda 2000ui, but my "boxed" 6.5hp 3500watt Chinese generator is darned near as quiet from 25ft as is my "un-boxed" Honda.
BTW, I don't think you'd hurt your Honda by directing the exhaust into a bucket as shown. Just make sure the generator exhaust is above the water level, and drill a small hole (1/8" or so) in the vertical portion of the tubing above the water level
to preclude developing negative pressure that could cause water being drawn back into the engine. Very little exhaust or sound will come from the hole, BTW.