My son was partially homeschooled. He was/is exceptionally bright but we homeschooled him because he was severely dyslexic and wasn’t learning to write at a level that matched the rest of his talent. I organized his homeschooling, which was a combination of tutors, a university school summer class, and one thing I did with him. He took art, social science and lab science at school but did English and Math at home because he needed to learn to write and HS math was trivial for him (he did junior honors math in 3 hours a week for less than a semester).
On ECs, we are in a culturally/educationally rich part of the country so don’t have the handicaps you are confronting. I agree that ECs probably matter less than people think but the schools want to see that your kids have devoted time to things outside of school. He could use his school’s activities because he was in and out of school and his passion was moot court. We bundled his out of school interests into some interesting activities that could be categorized in part as ECs. He was always interested in games of strategy and took a course from a home school cooperative on European board games and then designed a couple of games. He had a group of kids with whom he played weekend long game of a game called Diplomacy. I described those things together as an EC. He was working on coauthoring a fantasy coming of age novel with his much older author cousin/tutor. His coauthor had gotten a very positive read from a publisher, which we submitted as part of the application, but then she got some kind of writer’s block and somehow didn’t want to finish.
You might be able to bundle things like a reading group to read all of Shakespeare as a compelling EC.
He took a gap year and did his applications in the gap year. He also participated in a political campaign and research at a local university in that year. You could, if you wish do that to help with the ECs, but I don’t think it is necessary.
Several schools had an explicit section where the organizer of his homeschool program explained what they did and why. Interestingly, a couple of the schools asked for my recommendation, which I did with some care. I was fortunate to have attended and taught at some of the country’s most prestigious universities and could judge him relative to students at those schools.
For LORs, he got one from the university summer school class he attended, one from a social studies teacher at his HS, one from the Deputy Superintendent of School who suggested the partial homeschooling, and one I think from his math tutor. Plus the one from his dad.
I don’t know that the experience is entirely comparable as we live in an educationally and activity-rich environment. From a stats standpoint, I think his SATs were 1560 and the ACT was 35. He did not retake. He did very well in the HS classes he did take so his GPA from courses at the school was quite high. We didn’t grade home-schooled courses (except the one he took at an Ivy summer school). He hated the idea of visiting highly selective schools and falling in love with one and then getting rejected as there was a 10% chance of being admitted. So, rather than do that, he offered to apply to more schools. He applied to 15, got into 10 (I think as this is a few years back), was rejected by two and wait-listed by three. Of the 10, his top two were an Ivy and a “Little Ivy.”
I think in those days, they broke the schools down into reaches, matches and safeties. In his case, the reaches were Amherst College, Williams College, Brown, Princeton, Yale, Harvard, Dartmouth. The matches were probably Wesleyan, Bowdoin, University of Rochester (this is a school I also really like), Vassar. Safeties probably UMass Amherst, Sarah Lawrence, Bates, a school in DC (either Georgetown or American University).
I don’t know if this is helpful as our experience is a little dated and we live in a culturally and educationally rich part of the world, but I hope it helps.