One possible way to rescue a kid from a program is that some European countries have an age of majority of 17, not 18.
So the trick would be to obtain visas for the rescuers and kid to live in such a country, or stay in such a country for a year or however long until the kid turns 18. And have either the paperwork ready for a passport (somehow) or perhaps the kid already has a passport and its possible to get hold of it. Then you could take off and enroll the kid in school over there and make very sure the kid looks like the perfect model of propriety, and the kid's an adult and the European courts are going to take a dim view of shipping him back against his will. And the State Department and American courts are very reluctant to enforce the law otherwise. I suspect they'd be even more reluctant if the kid was in school, getting good grades, and wanted to stay right where he was.
I don't know if this would work, but it might be worth looking into if you're trying to rescue a kid who's 17.
Europe is really harsh on religious nuts, and if the kid is a model citizen, making good grades in school, following all the rules, and actively learning the local language and can talk intelligently about the wonderful language and cultural opportunities in Europe and the cult brainwashing in the facility, well, you're not going to get the kid out of Europe with a crowbar.
One way to do it if the rescuer had lots of money would be to buy the kid citizenship in Nevis and St. Kitts and get a N&SK passport to get visas and travel on. Belize and other countries that formerly sold citizenship don't do it officially anymore because the US gov't. hates it as a tax dodge, but it might be possible to still get it done "under the table"---especially if no tax dodging is involved and the Carribean nation can semi-credibly claim that the citizenship was issued to the kid as a refugee for humanitarian reasons and all that money was just a "donation" from a friendly individual.
If the kid has such a dual citizenship, you can avoid all the problems of getting the kid's US passport. Drive to Canada or Mexico and fly to Europe.
Iirc, citizenship would probably cost in the neighborhood of $100k. Cheaper to hire a good lawyer unless you've already exhausted all such means.
Timoclea