You'd think. There are a few decent doctors out there who deal with circadian rhythm disorders, but I'd recommend finding a good forum for sleep disorders online and asking for a local recommendation. I waited a year for my local sleep clinic and they were terrible. This included completely ignoring the year's worth of sleep logs I brought, which looked exactly like yours. A good sleep doctor will generally use light therapy, though darkness therapy is something I don't think they're up on yet, they're still at the stage of prescribing drugs. Which have their place, but are a bit silly when restricting blue light works a treat and doesn't have side effects!
Anyway, it's also possible that they might just blame it on the fibro/PTSD/what have you, I have CFIDS so I get that a lot.
It does indeed, although the sleep clinic I saw were completely crap about circadian rhythm disorders. All they were interested in was sleep apnoea and narcolepsy. I ended up writing a website about all this, look up In Search of Mornings and it will explain it all. Best of luck dealing with it, it's a crappy sleep disorder to have.