What you say about the intervals makes sense to me, and related to rajlego's comment as well it seems like major changes in activity level or timing take some adjustment.

I know what you mean about "different types of tired". It is rediculous how many different varations of being tired there are if you have serious sleep issues. I have the same thing about feeling completely exhausted and what I could only call tired but not being able to actually sleep. I have learned a bit over the years (I'm about 40) to tell when it is actually possible to sleep but I am never sure. This is the kind of thing I want to warn people about as well as the non-24 when people talk about trying unusual sleep schedules; it really can mess you up quite a lot if things go badly.

I have also noticed that every few years there seems to be a significant shift in how I sleep and I've heard similar from others with various sleep issues. I suspect it might also be the case for most people and seems like it would fit well with your interval descripiton.

I had at least two periods of severely disrupted sleep lasting years in my first couple of decades of life but didn't end up with non-24 until I tried free running sleep. Although thinking about it a bit more it wasn't fully free running for a longer period but more trying to advance what had become a very delated sleep schedule (mostly by means of not using an alarm clock until I was back on a schedule of sleeping during the day). It is possible it would have happened anyway in my case. And the "generally disrupted sleep" aspected that I still have due to insomnia and circadian desynchronization seems worse than the non-24 part, but still not having non-24 even with the other sleep issues would be preferrable to me. It sounds like you have a milder version of what I have.

I also sometimes have noticed that I am most alert and productive not long before bed, although for me most often a similar thing happens early afternoon when I am waking up before 9 (and I personally seem to do best waking up at about 7am). My guess is that it happens before bed due to the process that keeps us alert right before bed that somehow is extended, my guess is that is related to having not previously reached a similar level of alerness earlier in the day. I have been meaning to look into that process in more detail but haven't done it yet.

I've also been thinking that for me at least one of the major issues is that the process of waking up is not working correctly. When I get less sleep than usual I can these days sometimes avoid advancing my sleep schedule but not always and even not sleeping at all does not usually make it easier to get to sleep early the next day. But it does make it easier to sleep longer once I do get to sleep. Maybe once every few years or so something briefly happens in the morning right as I am waking up that feels like rapidly altering between being asleep and awake for a few seconds causing a distinct feeling and I am always much more alert than usual that day.

Have you used melatonin at all? I find that oral or sublingual melatonin cause me to wake up a couple of hours after I get to sleep and not be able to get back to sleep (melatonin patches do not cause this but do not help at all getting to sleep, only staying asleep longer). This happens even if I take a small amount of melatonin a few hours before bed, meaning it should all be out of my system before I even get to sleep. I wonder if there is a "spring" aspect to the wake up mechanism such that it can be improved even before getting to sleep.