I guess you know that a "neck jerk" may be a secondary symptom, to try to relieve tension; or, could there possibly some neurological problem, here? How long has this child had a "stutter."
You mentioned "blocks" at the beginning of sentences. How long are his sentences and what are the circumstances at the time of the tension? Are you in a clinic or seeing him at his home setting?
I am interested in helping you if I can but I need more information. Many things can appear as stuttering but at the preschool age most kids are at the emerging or beginning stages. This child sounds like an advanced stutterer. So, I need to understand.