Colin and David, I’ve been a long time Feedly user myself and certainly feel your pain. (And in particular, I’m a bit irked that I can’t seem to get Feedly to discover alternate RSS Feeds being broadcast from my site to provide consumers with more options about what content they’d like to consume from my site, see also: )
While slowly hacking away at IndieWeb philosophies, one of the big issues I’ve always hated was using an outside feed reader that wasn’t directly integrated into my own site. I’ve played around a lot with which has some great IndieWeb features, but doesn’t have the massive developer team behind it that Feedly does.
Recently while doing some alternate research I also came across the WordPress plugin PressForward that was originally designed for journalists and academics, but in short is actually a built-in RSS feed reader that you can self-host as part of your WordPress install. I’ve been loving its general functionality and also use it somewhat like a self-hosted version of Pocket/InstaPaper as well, so it serves multiple uses. While it may not have everything that Feedly does, it’s incredibly functional, and better, it’s open on Github with lots of documentation, so you could potentially add the features you want. I’ve written a bit more about it (including some useful links) here if you’d like to explore it a bit more:
Like both of you, I’m always eager to hear of other options should you come across them.