Dave discovered that Feedbin can also produce an RSS feed for all your likes. Likes is a feature of Feedbin, and fortunately also NetNewsWire, which syncs the likes back to Feedbin. You have to flip a settings switch in Feedbin, but then you get a URL for your likes. Here’s mine.
Unfortunately, the feed isn’t CORS ready, so you’ll have to run it through a proxy — but it’s doable.
Also, did you know you could style an RSS feed?