After some hours of weekend work, there is a new beta (version number is 0.6) of Radio Paradise for OS X. The application is now a menu bar application, runs completely from the menu bar (no icon, no UI needed). I’m still not so happy for the buttons but for the rest it is quite usable.
As usual, the source is available on GitHub. If you want to test it, grab it from here, unpack the zip and copy the application to the /Applications folder (not strictly needed, you can run it from everywhere).