I've been lurking for a while and wasn't going to join the discussions until I'd finished the sequences, but it doesn't look like anyone has mentioned the possibility of just switching to a 28 hour sleep cycle. I've wanted to try one for years, but college or work always conflicted.
Basically, you go to sleep 4 hours later each night. Your first bedtime is midnight, then 4AM, then 8AM, etcetera. By the 6^th sleep cycle, you will have slipped back a total of 24 hours. Because of this, the crossover point occurs after 7 days. This means it is possible to maintain a relatively normal schedule, so long as you can leave work early on Mondays, and get to work late on Fridays due to sleep.
Xkcd has a rather nice graphical illustration, and the comic explanation is a bit more thorough than I was.
See also c2's 28 hour day and 36 hour day
I agree with tut that this doesn't work as any kind of regular schedule. Possibly temporary when you are young and have enough extra power to burn.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)
3. Open Threads should be posted in Discussion, and not Main.
4. Open Threads should start on Monday, and end on Sunday.