Andy,
Thanks for your feedback. The rack packaging describes the rack as a "seat post mount" rack, but I do know the picture I have is definitely the rack in my hand. "'P' shaped surround clamp" also seems to describe what came with the rack, though if those aren't shims, then I have no idea what the instructions on the packaging refer to.
I think I'll have to take everything to a bike shop and see what they can do. Your feedback regarding the picture I've posted, while very helpful and thorough, don't at all line up with the instructions that came with the rack, so unfortunately I'm still stuck. Thank you very much for your input though!