You will be able to get divorced if you have been separated for one year and one day. These delay tactics will only work for a little while, but not forever. He is only delaying the inevitable and ultimately spending more money than necessary. I’m not sure how many times they can file for extensions.
My suggestion is to wait to move in. If your ex is the type to sue for everything then don’t give him any more ammo than he may already have.
The situation would have little to do with a custody order unless your ex has filed to modify custody. Even then cohabitating in NC is no longer illegal as long as you are not married. He would have to prove he is the better parent for custody to be taken away.
It sounds as though he’s grasping as straws and trying to drag this out so that you suffer. Wait until the divorce is final to move in.