I wouldn't run it in that compartment. No matter where you run it I would be careful with exhaust modifications as I have worked on a couple generators that people tried to modify and it started to melt the control panels and surrounding plastic. The heat cant escape.
I went round and round with that whole issue. It was a matter of using 2 generators and adding extra fuel tanks etc or getting a heavy unit. I went with a remote start Honda 3000 bolted into the truck bed with an insulated metal enclosure and lid. It has a 12 inch axial fan and vents on the enclosure. Wife can just push the button and dry her hair or run the ac. I dint want to keep messing with anything. Fuel it and change the oil. OH, AND dont drive away with it plugged in!!!