Why does it matter that they were system sessions? The important thing to remember here is that these sessions can not be KILLed. So because they were holding locks on the database (And somehow even though it was in single user there were multiple sessions with locks in the database. Don’t ask me how.) I wasn’t able to get that exclusive access I needed.
Interestingly when I tried to do the ALTER instead of just hanging I immediately got a deadlock error. I spent a little while trying various things and searching through forums before I went for help on twitter using the #SQLHELP hashtag.
Read on for the answer, including how deadlock priorities saved the day.