You sound exactly like me. I have had issues with my sleep basically all my adult life (I'm 29 at the moment), and in the later years I have found it less difficult to actually fall asleep and the big issue is that I will wake up everyday several hours before my alarm goes off. Like you I go to bed roughly the same time every night (around 11), I don't have any caffeine after ~10 in the morning, I try to exercise 4-5 times per week (although some days my head will be throbbing due to the tiredness I am feeling), so some weeks will be less. No smoking, and I drink seldomly. Reading this forum I am nowhere near as bad off as some people as I would say I average 5-6 hours a night, but it is enough for me to not feel properly energized.
I have tried all the common tips that I've found to try and combat this to no avail. I have tried TONS of different drugs, both prescribed (Propiomazine, Promethazine, and a few others I cannot remember the names of right now) and natural substances (melatonin, 5-HTP, GABA, Lemon Balm, Chamomile, Valerian Root amongst others). The only one out of these that I have found somewhat effective is Promethazine, however I can no longer get a hold of these where I am living as they have been out of stock of all pharmacies for the last year or so. I can't say what will work for you, but if you can get a hand on some it is what has worked for me to be able to stay asleep until my alarm goes off.