Though I might have some concerns.. Think of this.. Is your roof strong enough to walk on? (Mine is but I'm in an "A") if it is, then you have perhaps 1/2 square foot of feet. more or less. So double your weight and that's the Pounds per square foot you put on the roof.
Now, figure out the weight of the tire and wheel, (Less than you I'll bet on a 350, I've changed many a 350 tire)
And look at how much will contact the roof (more than a square foot)
Nuff said?
NO, as it turns out not a nuff said.
i'd worry about the increase in height, The fact that it will be hard to check the pressure, and the fact the tire will be exposed (Unless you put a hard shell cover on it) and thus will age very fast.. >I'd sling it down below or use a hitch-hauler for it.
There are companies that make tire carriers that fit a standard 2" receiver and extend the receiver for hooking up whatever you tow... Car,,, Boat.. Trailer with golf cart on it
Oh, saw one the other day.. Guy carries his golf card on what looks like a lawn trailer (Flat bed, big tailgate that folds down into a ramp for loading, bit shorter tail gate than the lawn trailers though, stronger too)
Well, to park the trailer,,, He has a hitch on the golf cart!