I have terrible trouble sleeping and not much of any discernible circadian rhythm, but not as bad as the OP. I have no choice over when I sleep: sometimes it's during the day, sometimes at night. Sometimes I stay awake for over 30 hours. Falling asleep always takes me a few hours, unless I've been up for a very long time, like 30 hours or more, and sometimes I can't fall asleep even then.
I do tend to develop some slight pattern that lasts for a few days or even weeks at times, but it's always sliding, usually getting later and later. I'm pretty good at staying asleep once I do fall asleep, though if something wakes me up I usually can't go back to sleep.
Since I don't have a job, I don't have to be up at a particular time, and if I had to do it I wouldn't be able to. If I have an appointment to get to and I have to pull myself out of bed after just a few hours of sleep, or no sleep at all, it's crushingly hard to get through the rest of the day.
I have never been able to take naps, because it's so difficult for me to fall asleep, and i have never fallen asleep unintentionally, like on a car ride or a boring lecture.