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If you're going through with link removal and building a disavow list, you might as well log all the outreach efforts and results - it really doesn't take that long. Just note when you sent emails, when they replied, what they said, and if the link was removed. I'd upload that to Google Docs and include the link in the disavow file so on the off chance a real person looks into your site, they'll know you did the work.

I like SEM Rush. It gives you daily ranking updates for your keywords and allows you to monitor the serps for your keywords. I actually find the moz raking a little poor in comparison, mostly because it is only updated weekly. But I do look at both to make sure they correlate as much as possible, and they seem to. I spot check the SEM Rush rankings against searching manually every now and then too to make sure its accurate. So far it has been. I have used it for just over a year. All ranking tools have limitations - country specific,  data center differences, google testing stuff, etc etc. Only way to be 100% sure what the ranking is is to manually check (with a 'clean' browser as mentioned by someone else), but I bet you (like me) have better things to do with your time! Be interested to know what you choose and how you get on with it. Best wishes, Amelia