mounting a portable gen in a gen housing on TH - why not?

The exhaust extension is a concern. That will put more back pressure and I can see that resulting in shorter life. I've used one of the Gen-turi RV units, it doesn't any back pressure since it's the warm exhaust that flows up the "chimney". Above all you want to make sure that you are not getting exhaust fumes inside the RV. Check the location of your C0 detector and consider mounting one in the bedroom closer to the generator area.