I don't think my similarity is anything as awful as yours (I feel for ya)…but I suffer from something pretty comparable, but different, even somewhat opposite.
I will often force myself to “stay up” even when sleep deprived not to do anything constructive, but simply my mind won't let me. (There is more to this, but I'm trying not to be too wordy.) Often it is time specific. It usually has nothing to do with the usual “force” yourself up for something fun or work or school.
But the anxiety aspect def. extends to my sleep life–ranging from much of what you described, to my persistant love-hate relationship with nightmares. I don't even think I could really share any of them without severely censoring it, but they are pretty awful. Because I often lucid dream, I can control certain things, but there is much I can't control, and recently (in the past few years) I have lost what used to be my saving grace of having the ability to “force myself awake” since I am usually aware that I'm asleep. It gets very scary to the point that I will deny myself desparately needed sleep if/when I do wake up.
My brain also has gotten very tricky on me, I will through the course of any given nightmare (for lack of a more specific word) my brain will convince me I am awake, by allowing me to wake up in the dream–usually several times as I try and try to actually wake up, because my brain keeps trying to convince me that I already have woken up (environment, recreation of literally waking up, having long conversations with people in my dream about whether I am awake or asleep, etc.) So when I'm in a phase where I'm experiencing this I am severely afraid of going to sleep or back to sleep.
It is also highly common for me to wake up (sans bad dreams) in full on panic attack.