As for registering through an umbrella school vs. local superintendent, it’s really a preference, I guess. The laws are different. If you register through your local superintendent, it’s “free” but you must follow the state “homeschool” law which includes testing in certain grades and also can make you ineligible for some scholarships. Also, depending on who is in charge at the superintendent’s office, they might feel privileged to more information than they’re entitled to. Mr. _____ in my county seems to feel he has the authority to approve homeschooler’s curriculum, which he does not. If none of these things bother you, there is no reason not to register locally.
When you register with some umbrella schools, you are not “homeschooling” according to the state. You are considered a satellite school. My boys are on roll at Gateway and I am considered on faculty. It changes nothing we do at home, only in the eyes of the state. We are also not exempt from some of the scholarships and funding because we are technically not homeschoolers if that is important to you. (Laws are changing all the time and I am no longer on the THEA board, so if this has changed, I am unaware.) I also do not have to test because Gateway does not require it. I can if I choose (I don’t) but it’s not required. I only submit the registration form each year, which includes subjects and curriculum (and they are perfectly fine with listing “living books”), grades and how many days we’ve “done school”. That’s it. When my sons graduate, they get a transcript and diploma from the school.
Do your homework. Read the requirements for each of the laws. Don’t be afraid to ask questions from the umbrella schools. Make an informed decision. And then proceed in peace.