The preference of the child may or may not hold weight. In my experience, it is best for the kids to leave them out of the conflict as much as possible. A 12 year old may have a hard time explaining their reasoning and if the judge detects coaching by you it could get worse for you. Basically you are asking a 12 year old to fight against his flesh and blood in order to advocate moving away from his own mother. That has a lot of negative consequences.
As Sy said, your best chance is to get the mother to agree to this, but there is another way. You may not have the right to move the child away, but you do have the right to relinquish your half of the 50-50 split and move yourself away, leaving the child behind. I know this is not what you want, but if you can convince the mother that you are moving, no matter what, she may back down and give you custody, knowing that her only other option is to take custody herself.
Generally with move-aways, the grass is not as green on the other side of the fence as it may seem. The child will find himself doing a LOT of travelling and losing out on a lot of vacation time among any friends he may make in his new state. Living with parents in different states is a horrible existence for children. Judges know this and they are not easily convinced by children who really don't know what they are signing themselves up for.
My advice: either stay put or get the mother's agreement. Otherwise you are most likely just wasting money and energy, and at worst, you are really making a mess of your son's life.