Given the assumption that a Ford chassis is a Ford chassis, and that the under coach storage set ups are not that much different, for me, if it fits, it can get stored there......
I've never even considered that heat would be an issue, and if it would be, I cant imagine if it was, that it would be significant past the first bay that is closest to the engine and tranny, which I have not observed, but again, never paid any attention to anyway (nothing has melted.......). Now, maybe there is a clearance difference between coaches in the storage areas, so maybe your first run don't put anything across on the first bay and check out if there is any significant heat.
I have several different types of plastic bins, bag chairs and beach chairs, fold up wagon, etc. We also have a pass through that goes all the way across between our Genny and Popane tank that my 7'8" surf board can fit into to!
I have not had any problems with items shifting side to side and falling into the main bays (not like you are cornering at 1g!). And I arrange things so that they is not that much room for them to shift front to back.
2015 Tiffin Allegro 31SA, 24k chassis
2015 Jeep Cherokee Trailhawk