Rather than dropping music tracks onto the background area, I find it more efficient to drag each track directly onto a video clip. Instead of filling the whole background, a thin green bar (ribbon) will appear under the video thumbnails after you drop the track. The bar can be dragged anywhere in the project. The ends can also be dragged inwards to shorten the track (and dragged out again if necessary). You can also view the waveforms (if turned on) and easily adjust volume levels and fades within the timeline.
This method means that you don't have to use the "Clip>Arrange Music Tracks" menu item (in fact it is greyed out if you don't have any floating background music). In iMovie, the bars/ribbons are referred to as "voiceovers" and can consist of music or, as the term implies, voiceovers (recorded speech using a mike). The bars can be either green or purple, depending on their source.
I experience the same exact problem with 2 iMac's (mid 2011) running mountain lion and iMovie'11 9.0.8. Unable to rearrange background music. I was able to use this feature without problems a few updates ago. Since the original poster mentions version 9.0.7...maybe that version introduced the bug.
Although your solution is a good one, I like the feature iMovie has for rearranging background music. It is very fast and great for trying out multiple tracks for a video. Rearranging them is simple...if it worked.
One of those updates introduced a bug. But not enough users are complaining...so it probably won't get heard. It's a shame because I edit a few hundred videos each year...and this feature allows for fast music selection.