BazQux Reader supports Fever API now. This means that any mobile or desktop app with Fever support can work with BQ. Remark that it's not an official support. So if something goes wrong please ask me not the app developers.
First of all you'll need to set your password again even if you have set it earlier. Fever uses different password hash algorithm and I'm not keeping passwords on my servers -- only hashes. So please go to Settings => Mobile login and set or change your password:
(it can be unnecessary to reset password if you have used reader from mobile apps during last few days).
And now you can setup Reeder:
For more security you can write https://bazqux.com instead of simple bazqux.com (defaults to http).
Due to Fever API limitations starred items are synced only when they belong to existing subscriptions (items imported from Google Reader or items from feeds you have unsubscribed won't sync).
Press uses suboptimal syncing algorithm so first sync can take a while before you start seeing unread items. And Press syncs only unread items from last week by default (I recommend you to adjust this setting to a month and recreate Fever account). I'll try to contact Press developers to improve their syncing and request an option to keep all unread items without time limit.
ReadKit redownloads all unread items on each sync. So it can sync for a while when you have many unreads. And sometimes it hangs for a minute on restarts. It's already fixed in ReadKit beta (thank you Balazs!) and will be available on the next ReadKit update.
And Reeder just works great as expected ;)