Strange situation on rear brakes - 67 Barracuda

Where do the drums hit? That huge outer ring could come off and not hurt a thing

I cannot see in your bottom photo........how far do the shoes come to the INNER wall of the drum? Now, you'll have to have them turned, as the shoes will have "worn in" on the drums, but if you can clear the outer problem on the backing plates, will the shoes clear the inner part?

Also, you need to have someone with a "drum mic" (or other accurate measuremen) check that the drums are not too far oversize. "the standard" default oversize used to be .060