It took longer than I expected, but I have a self-hosted installation of FreshRSS which I can access via Reeder on macOS, iPad, iOS and the web. This install has been on my to-do for a while. If FreshRSS performs well on my server, I may cancel my Feedbin subscription.
Peter, this is excellent work. I love how these IndieWeb technologies can enhance a website. Out of curiosity, I’ll take a look at FreshRSS but I doubt that many RSS readers support it. Maybe someday, things like this will be trivial for the non-technologist (aka people who don’t do their own oil changes).