To answer a few of the questions asked in the comments:
My interpretation of what the combo algorithmic and manual efforts is this:
-One of Google's paid link algorithms (possibly a new one or possibly an existing one that was recently tweaked) flagged some of the links or one of the link networks. This caused those links to no longer count towards PageRank credit (and possibly causing some of the initial rankings drops, such as the ones from position 1 to position 7).
-When Google was alerted to the issue, they took a closer look and on manual inspection found not only additional problematic links but also other spammy issues (if you follow the link in my story to the blog post by the guy who helped NYT with the investigation, you'll see that the SEO firm set up doorway pages and that the jcp pages themselves have keyword stuffing and hidden links on them). Based on that manual review, Google added a manual penalty to the site.
That's why my conclusion is that once they fix the issue, the manual penalty will be removed and they'll rise a bit in ranking position. But since the algorithmic penalty simply (I'm speculating) caused some of the paid links to be devalued, there would be no "lifting" of this penalty.
It is very disheartening that something so vital to business success (understanding how to operate online; build a web site with good site architecture; engaging with searchers; solving their problems) is so much equated with these types of tactics.