I can totally relate to this. I have been known to "rest my eyes" in various spots while I am out and about. If you are going to get up at 3:30 or 4 every morning, then it only makes sense that you will be tired by 8 or 9 at night. I will often sleep through anything on TV if I sit and watch it after 8 pm. So I really don't even bother.
And even though I call myself an incurable insomniac, I am not really one after all. Because I am very awake and I function well.
So this will be my new catchphrase. I really don't need a lot of sleep. And I function just fine. Right now, especially since September began, I am busy, happy and sleeping 3-5 hours every night. I made the mistake of drinking tea at Alpha on Tuesday evening so I had to get up at 2 am to use the bathroom, but I have been going to bed fairly early (by 10-10:30 at the latest) and waking up around 3 or 4. This is plenty of sleep for people like me. I will catch a 6-7 hour catch-up every 7-10 days, and that's just the way I am. And I am absolutely fine!