People need different amounts of sleep. It sounds like you might need more. From what I remember learning, most people need closer to 8 hours. Is there any way to fit exercising in at a different time of day? Maybe on your way home from work? I need about 8.5 hours of sleep in order to feel rejuvenated and not tired. Do I ever get that? I can't remember the last time I slept that long, especially uninterrupted. Usually it's closer to 5-7 hours, interrupted several times. Makes me tired all the time. Right now I'm just wishing I could get 3-4 hours solid! Once I get that, then I'm going to wish for a total of 8.5 hours;-)
I think it makes sense that you stopped exercising so you could sleep more. It definitely sounds like you need it. I would also consider going to bed a little earlier. I know that is HARD to do when you need some quiet time. Maybe try to be in bed by 10pm at the LATEST, never later.
If you stopped exercising early in the morning, I imagine your body would get used to sleep better through that time...assuming you can exercise a different time in the day. Oh, and I also heard that even when you aren't asleep, just laying there is equal to 80% of what you get when you're actually asleep. So, it's helpful to lay there even if you are awake.
I don't think you sound like there is anything wrong with you physically. You really sound short on sleep to me!