I bungied the hell out of my hard case to the back rack, like thru the handle and across in such a way I knew it wasn't going anywhere. I drive a 4wheeler like a madman or so I'm told and still the best way to carry my bolt gun. Another good part is that when you get to where your going you have a nice steady flat surface to sit your stuff on like a mobile bench. Oh and I use a pelican storm for those adventures, don't think I would trust much less the way get from A to B on a wheeler.
Side note: if you do choose that route remember that there will be over a foot of gun case hanging off either side so weaving thru trees/cars/gates/cows/people/ anything else deserves extra precaution....
One last thought, how about a pull behind trailer like they use with lawn mowers etc just hook it up to the back put a cooler, guns, chairs, whatever you might need then when you get there you could unhook and have the wheeler free to run around.