Hello,
I use Moz, Ahrefs, Raven tools, Majestic SEO to gather the backlinks, this way i'm sure that i can get at least 98% fo them. THe links from the webmaster tools are very good because i'll see how many links are indexed and what is the current anchor text density. A penalty was released on the anchor text density just after the Hummingbird update.
You will receive a xlx file with two tabs as requested, full link list and links audit.
You can check my feedback and see that i've succesfully complete multiple projects simmilar to this.
We can talk more here, by ma-il or over sk-ype.
Best regards,
Cosmin.