I had the same problem (but with captivate so it is independent of development product).
CSS was the answer for me as well. Slightly different code but does the same thing. The problem I identified was that the player window allocates space for "Display activity name" and "Display course structure in player" even if you disable both of those in the scorm settings. So you end up with blank space even though both of those are off.
The solution would be to remove the space allocated if these features are disabled in the scorm activity settings. So that would be a core code change to player.php (I think)
Nothing to do with themes IMHO.