We use HomeLife Academy and LOVE them. I failed miserably at mailing things in, so the on-line component was a must for me. Also, they give family discounts which is nice for a large family with 5 enrolled like we have.
I have heard good things about all you mention though and I don’t know that you could go wrong with any of those.
As to ibkim2’s question, you are correct. You do NOT have to register with a church-related school (not really an umbrella but I call it that too). HOWEVER, if you don’t, then you MUST register with the LEA (local education authority which is usually the local BOE). If you choose this option, you should be prepared to show work, prove attendance and those types of things that I personally didn’t want to deal with. TN is not known to be homeschool friendly, so that is something to keep in mind though it has come a long way.
If you choose the church-related school option (which all of the ones the OP mentions are), then you choose your curriculum and basically cannot be bothered by local school officials. This was the best option for our family but I know some who go with registering with the LEA and like it fine.
You can get a lot of useful info. from the HomeSchool Legal Defense Association website about each state, and they explain the complicated TN laws very well. And yes, TN is making some changes, but from what I’ve heard the laws are even more favorable to HS families.