AJ, less room behind the WK bumper would actually make it easier. I would essentially be putting a steel shim between the rear frame and the inside of the bumper... probably one on the driver side and one on the passenger side. Then on he outside of the bumper mount a bar across. This bar would be extremely sturdy since it will be supported directly by the frame with as many bolts & stiffening plates as we'd want. You could then build the carrier off the bar; a pivot on one side and a latch of the other (like how the tiregate works).

If you ever wanted to remove the tire carrier, those mounting points could be used for another accessory, like a shackle mount.