Hey now, we night owls forced into daytime hours aren't deviants! <grin> After years of banging on various types of machines I have found some of the best technical support works at night. They're bored, and if the phone rings they'll just about jump through hoops to help out.
With a 24/7 schedule, you may also find those who are looking for weekend or evening/night jobs to supplement their income. There are a lot of people doing that right now, and I'm pretty sure the market is going to see even more before our economy gets fixed. Many support centers also have remote employees working from home who have a VPN or some type of terminal into the office. This would be a major bonus for people working a second job.
I wish I could help with the scheduling, but I've only dealt with a 24/5 schedule with 3 rotating shifts, and it appears that there are some good suggestions above.