I'm sorry you're having to deal with this situation. It must tug at your heart as a mama to have your son want to stay with you, but then feel compelled to make him return to his father. Divorce stinks for everyone involved! (I know from experience.)
Before you can make a good decision, you need to get to the bottom of WHY your son doesn't want to return to his father's home or why he wants to stay in yours (you may already know this but just didn't include it in your request) and WHY his father is so opposed to this idea. There are hundreds of reasons possible. Your son may be unhappy with a situation at school that has nothing to do with his dad. After you know the reason(s) why your son wants to make this change, then you will have better information for proceeding.
If there is a tough situation at school, and everything is basically okay in his father's home, then you can discuss whether a change of schools might be another alternative. If it's a situation in his father's home, again, see if that is something that can be worked out. As much as your heart probably wants your son to stay with you, it could be teaching him to run away from problems instead of resolving them, and that does not bode well for his future marriage. Then, if it can't be worked out, your ex might be kinder to you if he has seen that you tried to find a way to work it out for your son to stay with him, and you're not just trying to lure him away (he can have that perception, even if you're not trying to lure him away).
If it appears to you that having your son stay with you is truly the best option, objectively; then figure out whether you might be able to reason with his dad by having him focus on your son's best interests. If the dad can be motivated to understand and go along with even a trial period, then legal intervention can be avoided. It can't be in your son's best interest to get tangled up in a legal battle. That's the grown-up's problem, not his.
If you haven't already, ask your son what he thinks the reason is for his dad being opposed to a change in custody. You may get some good information, but keep in mind that this is just your son's perception, not necessarily the true situation.
Your ex-husband may not want him to stay with you if he'll have to pay child support or if he'll lose any child support that you're paying. So, consider whether you could support your son financially without any help from his father. Also, if will hurt his pride to have his son chose your home over his. To enhance your chances of winning over your ex to this idea, be sure to never refer to this change as "choosing ME" or "he wants to be with ME". Instead, focus on it being "coming to TEXAS" or "changing to my HOUSE". That wording might help it feel a little less personally against his dad. Try to keep the focus away from any negatives in the dad's home, especially of there are good reasons that are unrelated to his dad personally.
As far as "pressing runaway charges", one of the first things the police ask when someone reports a missing child or runaway teen is whether there is a custody dispute going on. They won't play that game, unless the child is physically endangered.
I hope that you can get to the bottom of whatever it is that is bothering your son about living in Virginia with his dad, and come to peaceful terms in your family. I wish you the best.
