I found that a short piece of 2x4 lumber made a good spacer. The tip of the 2x4 inserts into the channel of the rear cross-member of the spare tire hanger, and the face of the 2x4 rests against the U-shaped fender aft of the cable hanger. Essentially I've extended the tip of the U-shaped fender so it pushes the inside of the rim of the spare tire away from the differential cover. The 2x4 is 5-3/4" in length, and simple nail above the fender keeps it from falling out, while the channel of the cross-member quite naturally locks it in place. The block is oak, and I plan to replace the nail with a stainless steel screw, so it should have acceptable longevity.
I've inserted a couple pictures.
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2006 Ram 3500 4x4 quad cab long bed, manual trans, mostly stock.