Yeah, the frame on the outside is a good idea. Guys make stinger-type looking things for flop down carriers that are essentially like that. I could see it having a hinged arm hanging down, which could pivot out and act as a stop so the tire fell down and stopped at about bumper level.
I used to carry a dirt bike back there and that was probably 300lbs. total. You could tell. I've been looking at narrower tires for just that reason.
I've also carried one on a roof rack right over the cab. Noisy, and I'm not sure the gutters are up to the strain over time. And a real PITA to get the tire off. Especially without it going down through the windshield