Q) Are all of these links from the original article site linking back to us, now considered negative SEO links?
A) Yes it is!
Q) Would this be a good reason to actually use the Disavow tool?
A) Exactly you need to collect all urls which you think is bad and impact negative seo
Q) Has anyone had a similar situation and used the Disavow tool and had success with it?
A) I have been go through all the bad links and sent it to google, and somewhat a little success in search ranks.
Q) Should we remove the Articles from the Article Sites?
A) Yes, if possible