A good start would be to write your own jPlayer GUI, so that it can be compliant with your requirements.
If you insist on modifying blue monday, a good idea would be to absolutely position some key controls, so that you know exactly where they will appear on the screen. You can also hide other functions, and have them appear progressively as the viewport becomes larger.
You most definitely need to write conditional CSS for these <li> elements in the jp-controls <ul>:
jp-previous
jp-play
jp-pause
jp-next
jp-stop
jp-mute
jp-unmute
jp-volume-max
By writing your own GUI, you can tailor your player to match your app's style exactly.
For a preview of mine, go to http://next.tjoonz.com and click the "Take tour" button (silent mp3 will begin playing, i am aware there is no audible sound at the moment of writing).