I have narcolepsy, which is different in cause but results in a lot of the same symptoms, such as tiredness and severe headaches during the day. I'm currently taking nuvigil, which is a nootropic specifically for narcoleptics. If you haven't had a sleep study yet, I recommend doing it. It's not by any means pleasant to have a bunch of diodes attached to your body for an entire day, but they'll be able to tell if you have a dysomnia that could be affecting your ability to slip into non-rem sleep and function during the day. Without proper sleep, people are disposed to headaches and fatigue. With the nuvigil, it's truly like night and day for me, so a sleep study may be worth your time.
Also, I recommend some kind of sleeping pill. Lunesta and ambien can be really heavy and last a long time. The first time I took lunesta, I slept for 18 hours straight. Ask your doctor about roserem, because it's prescription only (not because I get paid to tell you to ask your doctor about it like every drug commercial haha). The roserem was mild enough for me to be able to wake up the next day and function.
I'm not sure what side of this issue you're on or where you live, but marijuana is unbelievably helpful in restoring non-rem sleep, which evades me naturally. If you live in California or another legalized state, this might be worth considering.
As silly as it may sound, even your mattress could be causing some unrest. If it's old or too soft or firm, your brain may be responding to the body's slight discomforts and evading restorative sleep stages while maintaining unconsciousness. You're therefore unaware any of it even happened! Remember, it's all about the non-rem, baby. :P
I wrote this in ignorance, following the report writing standard of assuming the reader hadn't done/ didn't know any of it yet. I just wanted to cover all the bases I could and offer suggestions and possible easy fixes for treatable differential diagnoses. I hope it helps and I'll add more if I think of it.
p.s.- I really like your green fuzzy guy. The slippers are outstanding.