I haven't done any research, but I have been doing a lot of thinking on homeschooling.
It almost seems that the very idea of establishing a "curriculum," or a, "class" or "session" seems to make one shudder almost immediately. Labeling an education, separating it from regular life, makes it seem very undesirable.
Why put a label on it at all? Why not actually mingle it into daily life?
Perhaps one scenario could be this. You need to teach your child multiplication. Perhaps you could say that in order to play with this ball, you must first play a game with me. If you can count all of these apples before I count my apples, you can play ball. While the child's counting them individually, I could set mine up in groups of 4 or such, and multiply to get the answer quickly. The child will be dumbfounded, and ask how I did it. I will then show him how, by explaining multiplication to him, and possibly division. Then I would let him try it for a while. Then we'd play again, and I'd let him win
There! no mention of schooling, or classrooms, or education! He didn't even know i was teaching him anything, just showing him a trick.
I'm not sure if this will work very well on the more abstract stuff, like rhetoric in literature, but I think it would be a start. I just think that if you are going to teach something, practicality, like using mulitplication to find out how many real apples you have, is important. It makes it seem less schooling and more practical.
True, you need to have a bit of flair for excitement and the dramatic to keep it interesting, but I guess you could work on it. These are just my ideas.