Can you by chance hang the tire from the underside of the tongue right about where the tilt bed clamp holds the bed down? I have a buddy that had a Triton that did that and it worked like a million bucks. By the way he towed with a pick up so the tongue was not close to the ground. I would think if you're towing with a car or mini van that might not work.
I just throw my spare in the back of the truck for the winter, keeps it out of the slop and keeps it from rusting out before you get a chance to use it.