I grew up in rural fly-over land, and my little farm country high school with a very high proportion of kids on the lunch subsidy didn't prepare me very well for engineering school. Maybe one kid every other year would attempt engineering school. My pig farmer father died when I was 5, but my mother managed to stuff enough money away even in the lean years that I had money for a cheap land-grant university.
As I mentioned, I wasn't all that well prepared. I remember one night when DiffEQ homework was kicking my butt, and said to my self: "Ether get this stuff under your belt, or go home an clean hog barns for the rest of your life." I chose option A. My wife's parents were dairy farmers. She was the guru of scholarship application essays... that paid for her undergrad degree.
So, I get what you are saying. I've lived it. My wife lived it. But between us we've accumulated 5 degrees, made some good investments, been in a couple of situations where stock options were pleasantly large, and yes, work is optional right now, even living at Silicon Valley prices. Pardon me if I don't appologize for accompishing what YC and HN are all about.
So your post is a little short on actionable solutions to the problems we both see as clear as day. Here is a suggestion: MathPath has a need-tested scholarship fund so that kids that can't afford the camp can go. Tax deductable donations gladly accepted. Join me in donating. Then spread the word about MathPath -- anybody can apply.
I bought math books full of words off the bargain table for as little as a dollar and, after sorting things out with his father, just gave my son the stack of books to read. No tests. No written work. No problem solving. Just read these books. That finally worked and he has a good grounding in math, though he can't crunch numbers. He is, as they say, calculator dependent. But he absolutely understands important concepts. To my mind, this is vastly better than a kid who can estimate to 8 decimal places in their head, but can't grasp GIGO (garbage in, garbage out).
A great resource for "mathy" kids is Art of Problem Solving. https://artofproblemsolving.com There are free resources, their math books are outstaningly excellent (well, they could use more excercizes, but the exposition is superb), and they have online classes. The online classes are run with a live chat room that typesets LaTeX. The pace of the classes is blistering, so not for everybody. But you can buy the same books for cheap and use them at home at a pace that is right for your kid.
We used AoPS as the main spine of our child's math curriculum. At the time, it topped out at about AP Calculus, I'm not sure if they go beyond single variable calculus yet. Anyway, after that a local university let our kid take multivariable calculus along side the freshman engineering students. We were lucky to have that resource. Next problem: when your kid completes multi-variable calculus at age 13, what next? We did discrete math and freshman engineering physics, and counted them toward the high shool transcript.
Which is another problem homeschooler's face -- the so-called "mommy transcript". When it comes to college applications, it's good to have somebody in addition to mom posting grades to your transcript. The Uni grades in math and physics and recommendation letters from university profs helped the college application package a lot. For that matter, AoPS is well ennough known now that it is good on a transcript.
While I'm on math resources, http://www.mathpath.org is a truly wonderful summer math camp for kids in the 11-14 age range. Great faculty, great staff. Now would be a good time to think about applying for 2018. Just so you understand the scale here: My kid spent all of their spare time for two weeks on the quailifying quiz, attempting 5 of the 7 questions, a couple of those attempts were a bit weak. (A good solid attempt at 2 or 3 will get you in.) If you think your child might like MathPath, I'd encourage you to download the quiz now and let your kid start pondering the questions.