That issue has now been resolved! A recent code update means that InsaneJournal allows embedded media! YAY!
Even better, the embedding looks a little bit cleaner on IJ than it does on LJ. (I don't know why, but LJ embedding always looks a bit messy using Firefox/)
Behold Example #1 of embedding on InsaneJournal: Box.Net playlist
Behold Example #2 of embedding on InsaneJournal: My LastFM radio station