I suggest you locate the main duct lines that run the length of the rig. Ideally there should be two, one on either side making an 'H' layout. In reality, CR frequently shortens the one that would run above the bathroom as there is too little space to accommodate the skylight, vent and duct. But anyway, for your plan the other duct should run street side, opposite the bathroom, so you might consider adding a vent into that duct to direct cool air thru the open bathroom door. It will help cool the bathroom until the door is closed.
CR installs the vents after the unit is finished. They use a hole saw to drill thru the ceiling panel and thru the bottom of the foam duct board. The edges are sealed with duct tape and then the two piece plastic vent is added.
This only helps if you keep the bathroom door open most of the time, but that would also be needed for most other solutions also.
Texas Baptist Men-Retiree Builders member since '01
13 Silverado 3500HD D/A, 2wd CCSB srw, custom RKI bed
11 Cruiser CF32MK