I experience a similar sleep pattern, where I wake up after about 3 hours to pee, then two more times 90 minutes apart (also to pee) after dreams. After six hours, I feel the most rested and alert. But it's only about 4:30am. I'm warm under the covers and it's cold in the house, so I do deep breathing and breath counting. After a while I wake up again a bit groggy, but I can't delay, so I force myself out of bed.
I might start the day at 4:30am If I had something really fun to look forward to and if I didn't have a dog with separation anxiety issues.
I've been taking Nuvigil (Armodafinil) for several months and just added Effexor (Venlafaxine). The latter makes me want to eat a lot at night.
Before I started these meds, I'd be nearly falling asleep at work at 4:30pm. I'd even manage to drag myself to work in the morning while longing for the day to be over so I can go back to bed. So it's definitely an improvement.
My sleep cycle seems to be about 90 minutes, so I should adjust my bedtime so that the last 90 minute cycle ends when I need to wake up. I wonder if I should go to bed at midnight, then. Maybe I'll try it sometime.