While I'm not handbuilder, I will answer your question as to how we transport our RVQue gas grill which came with our Rockwood A126.
After it cools (over night or what ever) Gary leaves the hanging bracket attached and places the whole works into a large, heavy mil trash bag. Then "twist ties" the top closed to help contain any grease mess and cooking odor. When we travel it is stowed in our van (tow vehicle). Fortunately at home we have the luxury of space and can store it in the garage on a shelf and not in the camper. We do not store the grill in our Aframe because we are concerned about drawing up ants or other varmints into the camper.
If your bed lifts by hydraulics and has storage underneath, then maybe that would work for you.
Deb & Gary
2007 Ford E150 cargo van, 2012 Rockwood Premier A126
Everybody needs beauty as well as bread, places to play in and pray in, where Nature may heal and cheer and give strength to body and soul alike._ John Muir