If you have pop-ups and optins on every page, I would have to think that it would be a lot harder to convince someone to link to it. Especially since the pages where you have your optins (and probably receive the most traffic) are probably the same pages that you have your best content on as well that you'd be hoping to pitch in your outreach campaign.
Another thing to consider is that even if you break even on the first sale, you're still winning. All you need to do is create more content about other problems that target market may have following the same principle and queue them one after the other. For example if we target women that want to lose weight they may also have wrinkle problems, digestion problems, diabetes, aging problems etc. We can easily create a chain of issues we run the email list through, let them opt in for what matches their issues and make several sales to that audience.
Once you’ve gathered a list, put together a template outreach email (as you’ll be doing this over and over) that’s short and clear with expectations. Tell your potential interviewee who you are, what your podcast is about, and what you’re asking of them. Do a few test interviews with friends and family to make sure everything is being recorded at the quality you want and then book your first episode.
Win-win-win. The advertiser wins because they only pay when a purchase is made (as opposed to the shotgun approach of paying to advertise to the masses and waiting for a small percentage to actually buy). The affiliate wins because they make money while providing helpful advice. The customer wins because they get a trusted recommendation for something they might not otherwise have known about.