Your approach -- targeting home-schoolers who are "nonconsumers" of public K-12 education -- is exactly the approach advocated by disruption theory and specifically the book Disrupting Class. Using public education as analogous to established leaders in other industries, disruption always comes from the outside because the leaders aren't structurally able to do anything other than serve their consumers with marginal improvements.

ArtofProblemSolving.com is one successful example that's targeted gifted home-schoolers (and others looking for extracurricular learning) in math. I'm sure there are others. EdSurge.com is a good place to look for existing services, which you can sort by criteria including common core/state-standards aligned (you do have to register for free to get the list of resources). I also have thought about services that build on top of Khan Academy, but I wouldn't underestimate their ability to improve in that area. They just released a fantastic computer science platform. But they are a non-profit, so their growth depends, I suppose, on Bill Gates' mood and other philanthropy. To get to full disruption, it might take a for-profit with, as you suggest, monetization through tutoring and other valuable services.