HP, I would get a second opinion from another L. It sounds iffy to me to just move and try to get S later. Part of the reason is that if you leave w/o him, the new status quo will be that he is living with his mother and courts prefer to keep status quo.
What you would have to prove in court, is that it's to S's benefit that he moves with you. It is difficult to defend taking a child away from one parent. You have to prove that it will better his life, and that you have powerful reasons to move, reasons that are more important than seeing his mother frequently. You should also have a plan ready for visits with his mother at your cost.
There are specific criteria a court looks at to deem what is in your son's best interest. You may have a chance if you are the main caretaker and breadwinner, he has stayed more than 50% of the time with you consistently for at least 6 months, and you will loose your job if you don't move. But this is state-specific, so talk to a L who works a lot with custody and moves.
M 16 yrs, WH62, P54 3 adult blended kids EA 11/13, BD1 6/14 PA fall 14, BD2 2/15 Piecing 2015, BD3 12/15 Separated 4/16 WH moved OW in 5/16 Divorced 6/15/17