Ethan,
I went through the exact same thing. I was divorced when my daughter was 3. I remember one time driving over an hour to pick her up for the weekend (she was 8) and she started crying; she wanted to go home. I turned around and took her home; no bad feelings. We had a long distant relationship also for several years. It was me against the influence of her her mother, grandmother and about 20 cousins, aunt's and uncles. I decided I would not put pressure on her. I would lead by example. It didn't work. She came so close to leaving at age 18, but she told her mother she was moving in with me and she got the guilt trip with the "God's gonna kill you" speach. She called me crying, telling me she didn't want to die. At 19 I received a letter saying she was about to wed and I was not invited. She has not spoken to me for over two years.
I don't know what to say. I don't think forcing them to do anything will help. Everything you do, seen as negative by them, will be explained to them as the devil's influence on their apostate father, whom Jehovah can't wait to get his teeth into.
Keep the lines of communication open and going often. Go see them if you can afford it. By the time they hit their later teens, they may see things differently and question more. With you so far away your ex is driving the boat.
By the way... I have just moved to WA. SE side.
Best,
Bryan