Well, let's see...
1. Have you ever been professionally fitted? You may be slightly out of proportion and not realize it.
2. Ever been to a chiropractor? You might want to consider it, as your spine may be severely out of alignment.
3. Is the saddle in alignment with the top tube? I know, silly question, but if it is off by a couple of degrees, that could affect your posture.
The no-hands thing... my understanding is that the rake and trail have more to do with this than rider ability.