Did you in fact get a bike fitter to look at it already? I had a neck issue which I felt would be impossible to be related to my bike fit, but I went in for a professional fit (for other reasons) and my neck issue was 100% solved by bringing the handlebars a bit closer/higher.
If you have a good fitter already I would ask them for exercises. I have some posture problems which the fitter pointed out, and he gave me several good exercises for it.