Strategies for lead generation and sales to Bariatric Surgeons

I am working with a client that is focused on building and maintaining a large, national website that focuses on ranking bariatric keywords on Google Page 1. It works like this: We pre-rank a page on Google Page 1 for terms like, say, "bariatric surgeon Seattle" and then we reach out to surgeons (or clinics) IN SEATTLE who might be interested in "renting" that page. It's really a no-brainer: we charge a few thousand or so a month, and bariatric surgeries are expensive enough (sometimes 30 - 35K) that if the client got only ONE CONVERSION IN ONE YEAR from our page rental, usually they still come out ahead... MY PROBLEM: I need suggestions and help for lead generation and sales to these surgeons, who are notoriously hard to reach. We are working with an email list in one region, but we are also looking at LinkedIn Groups and LinkedIn InMail strategies... At this point, I need some solid help here. Not sure how to approach this market. And we do prefer some sort of social media play... Finally, if you feel that you have expertise in this specific area of selling online marketing products to surgeons, and you are confident that you could help us move the conversion needle, please reach out, and I might call you. Any help is greatly appreciated, and thank you for your time!