Cody, what you explained is kind of similar to my situation, the 11 sites I have are all Real Estate sites and they contain different "area" information (because they cover different geographic areas) but they share the same database of properties for sale.
We do have set different search results pages to avoid showing the same properties on every site, but, there is a link to similar properties on each property page which eventually the crawler ends up indexing all properties within the database so when you mention ..."every site had the same products"... this could be a similar situation.
As of now, I am waiting to see what happens next with my rankings, I guess I am a little lost on how long will it take until some signals are reflected on the serps, any idea?
Cheers and thanks a lot for writing about your experience with this.