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.
SUMMARY: Let's collect people who want to work on for-profit companies that have significant positive impacts on many people's lives.
Google provides a huge service to the world - efficient search of a vast amount of data. I would really like to see more for-profit businesses like Google, especially in underserved areas like those explored by non-profits GiveWell, Singularity Institute and CFAR. GiveWell is a nonprofit that is both working toward making humanity better, and thinking about leverage. Instead of hacking away at one branch of the problem of effective charity by working on one avenue for helping people, they've taken it meta. They're providing a huge service by helping people choose non-profits to donate to that give the most bang for your buck, and they're giving the non-profits feedback on how they can improve. I would love to see more problems taken meta like that, where people invest in high leverage things.
Beyond these non-profits, I think there is a huge amount of low-hanging fruit for creating businesses that create a lot of good for humanity and make money. For-profit businesses that pay their employees and investors well have the advantage that they can entice very successful and comfortable people away from other jobs that are less beneficial to humanity. Unlike non-profits where people are often trying to scrape by, doing the good of their hearts, people doing for-profits can live easy lives with luxurious self care while improving the world at the same time.
It's all well and good to appeal to altruistic motives, but a lot more people can be mobilzed if they don't have to sacrifice their own comfort. I have learned a great deal about this from Jesse and Sharla at Rejuvenate. They train coaches and holistic practitioners in sales and marketing - enabling thousands of people to start businesses who are doing the sorts of things that advance their mission. They do this while also being multi-millionaires themselves, and maintaining a very comfortable lifestyle, taking the time for self-care and relaxation to recharge from long workdays.
Less Wrong is read by thousands of people, many of whom are brilliant and talented. In addition, Less Wrong readers include people who are interested in the future of the world and think about the big picture. They think about things like AI and the vast positive and negative consequences it could have. In general, they consider possibilities that are outside of their immediate sensory experience.
I've run into a lot of people in this community with some really cool, unique, and interesting ideas, for high-impact ways to improve the world. I've also run into a lot of talent in this community, and I have concluded that we have the resources to implement a lot of these same ideas.
Thus, I am opening up this post as a discussion for these possibilities. I believe that we can share and refine them on this blog, and that there are talented people who will execute them if we come up with something good. For instance, I have run into countless programmers who would love to be working on something more inspiring than what they're doing now. I've also personally talked to several smart organizational leader types, such as Jolly and Evelyn, who are interested in helping with and/or leading inspiring projects And that's only the people I've met personally; I know there are a lot more folks like that, and people with talents and resources that haven't even occurred to me, who are going to be reading this.
Topics to consider when examining an idea:
An example idea from Reichart Von Wolfsheild:
A project to document the best advice we can muster into a single tome. It would inherently be something dynamic, that would grow and cover the topics important to humans that they normally seek refuge and comfort for in religion. A "bible" of sorts for the critical mind.
Before things like wikis, this was a difficult problem to take on. But, that has changed, and the best information we have available can in fact be filtered for, and simplified. The trick now, is to organize it in a way that helps humans. which is not how most information is organized.
Collaboration
Finally: If this works right, there will be lots of information flying around. Check out the organization thread and the wiki.