Hi Jesse,
First and foremost, you need to determine exactly what the messaging means for your site. Is it a warning which indicates that there may be a manual action applied to your site, or is it actually just a notification intended to tell you that Google is discounting unnatural links that have been detected.
The most efficient way to get an answer on this is to go the Webmaster Central forum and ask the question "Does this mean that my site is under a manual penalty?". (I would not discuss the links you already know are a problem, just the need for clarity in the messaging).
I have seen a number of instances where Google's John Mueller has taken a look at the specific site and advised webmasters that the message is actually just an advice that they have detected unnatural links and are discounting them at what they refer to as a "more granular level". If this is the case you do not need to lodge a reconsideration request, but you should take it on notice that your backlink profile needs some careful scrutiny and any troublesome links should be dealt with as soon as possible. Basically, it's a "heads up" and you should take it as such.
Second, over 10 months of providing phone support for rmoov.com I have spoken personally with hundreds of site owners who are confused by the messaging they have received or not received from Google.
From my discussions with these people I know that there are a large number of sites which have a manual action in place and have never received a message from Google of ANY kind. Clearly, not everyone who has a manual action applied is sent a message, despite assertions to the contrary.
On the more helpful messages, out of the hundreds of people I have spoken with, barely a handful have ever received one of these more helpful messages.
While I am sure that Matt sincerely believes the information he provides in his answers is accurate, the fact is that what is actually happening within the webspam team does not match his information. In my view this is the fundamental issue preventing most people from dealing effectively with their situation.
On the subject of removing the links, you have a bit of an advantage in knowing where the paid links have come from
First deal with these paid linking arrangements.
Since you mention that they have been acquired from sources that are likely to bring with them their own problems, I would not recommend trying to remediate those links by applying a nofollow tag. So, first job is to ensure that every payment arrangement that still exists has been cancelled. Record evidence of these cancellations by keeping screenshots and/or email receipt text.
Add any where there is no payment arrangement to your list to contact.
With the low response rate you indicated, the next thing to focus on is increasing the effectiveness of your outreach:
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Make sure the text of your email is friendly and personal. Remember that your email could well be one of hundreds already received by the webmaster that day. Show some understanding for their situation, explain briefly why you are making the request and ensure that you provide details of the URLs where the link(s) can be found in their site. Ask nicely and thank them for their help.
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Help the webmaster to tick their due diligence boxes (ensure that your outreach email originates from the domain you are trying to clean up, use a real name and provide contact information so that they can match them easily to information that appears on the site).
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maximize accuracy by obtaining as many different contact methods as possible (email addresses from the site and the WhoIs record, contact forms where you can submit a request, twitter handles, google+, facebook & linkedin profiles, telephone numbers, physical addresses). Use whatever works for you.
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send polite reminders at reasonable time intervals. At rmoov mail is sent every 3 days for the life of a campaign. Don't assume because a webmaster did not immediately remove your link that they aren't willing to do so. Again, your request could be one of hundreds ... sometimes a couple of gentle reminders will help.
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Pay particular attention to undeliverable notifications returned from your outreach. Some privacy protected domains do not accept mail, but will provide a contact URL that you can use to contact the webmaster.
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Document everything. Keep copies of responses and make notes on how you will handle those domains. e.g. "Webmaster advised a cost of USD $500 is required to remove each link. We believe this to be an unreasonable demand, so have chosen to disavow all links from the site at the domain level".
Finally, disavow only after all attempts to remove links have been exhausted and disavow at the domain level unless you have a very good reason not to.
Well, this is now way too long, but hope it helps.
Sha