Unfortunately, I doubt I have anything useful to suggest. I've been a very happy use of Feedly for years, but I don't know how well they do with accessibility or how screen reader-friendly it might be. The best I can offer is a list of web-based readers that I used to test that my links could be read, but if you've been on the hunt for that long then I'd guess you've already looked into all of these, and I don't know how accessible any of them are, either. But just in case it's at all helpful:

  - https://feedly.com
  - https://www.inoreader.com
  - https://www.newsblur.com
  - Feedbro, a Firefox extension
  - https://theoldreader.com (mentioned by you)
  - elfeed (an Emacs package, so not web-based)