So I whipped up this little shell script. As long as the video is open in iTunes (I'd let it finish loading, too), it will be able to copy it to your desktop. You'll have to rename it yourself.
cp -v `lsof |grep -i QTP| grep iTunes|awk '{ print $9 }'` ~/Desktop/currentmusicvideo.mov
[robg adds: There have been other hints here on saving the QuickTime temporary queue, but this seems like an easy solution.]

