Thought I'd share one thing I found that helped me identify which dupes were causing the problem, in case you didn't want to shell out $15 for the program linked above (or like me, are on a Windows box and can't run it).
First thing I did was identify all the duplicates from the iTunes store (the quickest way for me was to add the field "Purchase Date" in iTunes). Out of 3500+ tracks that iTunes considered "exact duplicates", this was about 60 tracks. I removed them from the library and moved them to a different directory on my computer.
Next thing I did was have to restore a cloud backup (unrelated to this issue. All my audio files turned to "other" and I didn't want to spend time deleting it, so I reverted to a backup I did to the iCloud last night). After I did a restore to my backup, I connected to iTunes to start to transfer music. I saw three songs get copied to my iTunes library - this was weird, because I never got the popup asking me if I wanted to transfer purchased from my phone to my library. Through trial and error, I have identified that these were the only 3 tracks that were causing my issue. In subsequent syncs, the iPhone kept sucking them down and putting them into my library, even though I have disabled match, show all songs, iCloud, and every imaginable setting on the iPhone. Frustrated that this kept happening, I factory restored and setup my phone as a new phone. I made sure the 3 culprits were not in iTunes, and the problem is gone - all cloud based settings are disabled and the phone is no longer attempting to grab these tracks from the iTunes store.
Struggling to find some common thread of what caused this, all 3 of my "bad" iTunes songs came from free downloads I got from the weekly cards they have at Starbucks, all circa 2011. Not sure if that is a coincidence or not, but I won't be taking any freebies from the iTunes store anymore.
It has now been 30 days with my new phone and I am finally able to use it. While I am happy there is a solution, this whole experience has soured me on Apple. Really unsatisfactory that the people on this thread and other sites had to brainstorm for acceptable workarounds while there is silence out of Cupertino.