I've tried
Moon+ Reader, on the strength of it apparently being the preferred reader of the team that maintains Calibre. It's pretty good as well, but I have a slight preference for the Kindle app. I haven't used Moon in a while, and it looks like the interface is a lot different from the last time I tried it (about a year ago), so it might be worth a shot.
ETA: I have read, but never personally verified, that Moon is compatible with Overdrive.