I think I located the problem and I am hoping that somebody can give me a confirmation or put me in the right direction. It looks like they put the cable over this little metal tab which is binding and scraping the coating off my new cable. I think it is preventing the brake from engaging.
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I no longer own the vehicle and the parking brake in my new Expedition holds on a hill, but I wanted to comment on this picture. It was confirmed that this is the correct routing of the cable.