I had to do something similar to this for an Onan Marquis genset for a gravel testing trailer. We needed to be able to run it in the garage, with a flex exhaust hose going outside through a port in the garage wall. What I did was to weld up a short exhaust pipe with a 1 1/2 inch pipe thread on the end. (I used--surprise--pipe for this. ) To that, I connected a male quick disconnect pipe fitting, and the female part on the flex hose through the wall. I did this because I had lots of surplus 1 1/2 inch pipe and fittings, not because I needed that size. You could use 1 inch pipe & fittings, I think.
You can get this stuff from Grainger or a really good industrial hardware store. The male end looks sort of like an immense, hollow, zerk fitting. The female end slips over it, and uses two eccentric cam locks with overcenter levers to hold fast.
This might work for you if you use a really short exhaust pipe going through the floor. Disconnecting to slide out the genset would require crawling under, though. You could also do up an exhaust line that comes up into the genset compartment, and you could put the connection there. That might create unacceptable genset compartment heat, though.
Also, most female ends come with a rubber gasket. You would probably have to replace that with heat proof gasket material.