Hi!
I feel I may be able to offer you some helpful advice as an (almost!) graduated senior from Texas who has been homeschooled her entire life and is applying to many of the same schools you are interested in.
Up until middle school, I was essentially un-schooled. My mom did make me take all of my core courses (so no skipping out on math, even though I wasn’t as interested in it) but when I got SUPER interested in studying strategies at the Battle of Gettysburg in the 5th grade, we camped out learning about the Civil War for probably around 2 months. Over those 2 months, I checked out almost every book about the Civil War at our local library (fiction and non-fiction), watched every documentary about that time period that I could find, wrote a 10-page essay about the Civil War just because I wanted to, and even bought a drawing book I saw at Half Price Books that was themed around the Civil War. So yeah, my education was definitely very…different from many other students for the first half of my life. 
However, once I entered middle school, my education became a lot more structured. I started getting more serious about math and science, and I realized that if I wanted to get into the schools I was interested in, standardized testing would be important- especially because I was a homeschooler.
I was thrilled to find out that I was accepted REA to Notre Dame a few months ago. I feel very certain, though, that my acceptance was largely based on the amount of standardization I had to back up the grades I had received as a homeschooler. I worked hard to get my SAT up, and I had taken 9 AP tests by the time I applied. I’m taking 6 AP classes this year. I also provided 3 SAT Subject Test scores as well.
Just about a week ago, I interviewed with Harvard. One of the first questions my interviewer asked after finding out that I was homeschooled was “How do you compare to public schoolers?” As soon as I mentioned my AP tests/SAT Subject tests/SATs, he didn’t bring it up again. That really confirmed my suspicion that standardized testing is HUGE for homeschooled applicants to top 20/Ivy League schools. Obviously, your SAT or ACT scores already matter if you’re applying to Harvard, but they become especially important when you’re homeschooled. It’s frustrating, but it makes sense that these schools want to see how you compare to other traditional students across the country.
So, here’s my thoughts on your application. You have a FASCINATING story, and I see tons of potential for super creative essays about your experiences traveling, learning, and pursuing your very unique passions. My main recommendation now would be to focus on getting your SAT scores up and taking some subject tests. You probably want to go for a 1500+ on the SAT, and take 2-3 subject tests that highlight your interests (literature and maybe world history?) Either way, just aim to create some of those “points of standardization” so that schools can more easily compare you to other applicants coming from a traditional public school. If you can get your SAT score above a 1500, I can see you being a very competitive applicant to many of the schools you mentioned.