I used to wake up at 4am every day to go to the gym. The secret is that I wouldn't break my sleeping schedule on weekends.
If you're staying up late on weekends, you're never going to be a morning person - Mondays will always be brutal, and you'll start feeling normal around Thursday/Friday only to repeat the cycle.
When I worked 12 hour shifts 0600 'til 1800, I got up at 0400. I always woke at 0359.50, and turned off the alarm just before its first beep. That's how crazy accurate the internal clock is. I'd always sleep at the same time, IIRC 2100.
Now I work normal-ish office hours I get up at 0730, work from 0900-0930 to 1730-1800. I could work earlier or later, and this means I'm a bit more lax at sleeping. Case in point, replying here at 2240 when I should be thinking about sleeping.
I think you can adapt to any cycle you like so long as you have the willpower to define the sleep and wake times, and stick to them. It only takes a couple of weeks and then it's second nature.