I think they might have been inspired by one of those sects, but there are enough differences that I think they're definitely their own tribe. The girls wear pants, the mom's wedding gown has bare arms and shoulders and make-up, etc. No minister at the weddings, just Elvis in a secular chapel....and nothing overtly religious on their page at all from what I can see, except for the common nativity Christmas decoration. No prayers, religous memes, pics of church community friends/events, etc. Very, very odd.
My theory too.
Homeschooling is actually more expensive. You still pay taxes for the public school district but you have to buy your own curriculum, equipment, supplies, etc. (I've never done it but know many normal people with amazing kids who have.). Even if you could write some of that off, and maybe in some states you can, it's not a way to make or save money. I think that is just more evidence of how crazy controlled these kids lives were.