So I was doin some thinking without drinking and looked at all the tire carriers that are for the stock tire sizes. I think our hatch on the 3rd gen could support one but not just mounted just to the sheet metal. So here's my idea for a worjaround .
First I would need heavier duty hinges and struts. The hinge assembly seems simple enough to reproduce for a decent machinist. But the hinges are also where the top mount for the frame would be attached.
For a frame a simple 1.5" tube should support the weight of a tire and rim. The 33" tires and rim on my pickup weigh in at about 80 each so frame plus tire assembly would be 100ish?
With the cargo door closed there should be enough strength in the hinges and the lower support (like how the Gobi ladder attaches) to safely hold a 33" or smaller tire without the huge addition of weight to a custom bumper and also having to swing your tire away to open the rear hatch.
Thoughts? I tried illustrating it in sketchup but that was a fail lol.