Bob-
I was thinking of using some sort of set up like this on my Sea Ray, which has a step-through transom door.
I don't have a Honda EU 2000i or larger generator, but a Honda EU 1000i instead, which only weighs 27 lbs. So far, I've managed to avoid refrigeration air conditioning on Shasta Lake, due in part to the low humidity. The smaller generator meets my appliance needs, at least so far.
The plastic box vs the heat issue would depend somewhat on the amount of air ducted through the box, but a stronger metal box could be used. There are some nice ones made to solve RV security problems that have the ventilation openings provided, and are made out of polished diamondplate aluminum.
That exhaust extension is a real sticking point, for sure! Need a way to duct it out the cooling air exit w/o touching anything.
When I run the 1000i on my CD-22. I place iton top of the 120 qt cooler which is across the back end of the cockpit. The generator is placed axially, down the centerline of the boat with the exhaust pointed toward the main motor and over the motor well, so that heavier than air gases will fall into the well and spill over out of the boat, due the the well's shape, and also to the usual wind travel direction over the boat.
So far, I've never set off my CO alarm inside the cabin, with the door open or closed.
Indeed, there are a lot of problems to be solved, and I may well find myself out on the swimstep with the generator afterall!
You probably don't know much about our ex-patriot, Red Fox, but he once owed up to putting the generator out in the dinghy overnight with an extension cord following the painter (lead line) back to the "mother ship"!
Joe.