Simple. Don't let them. My province has a math education program that would rank amongst #2-3 in the world, and you aren't allowed to run a private school with a different curriculum - at all, beyond a certain amount of enriched tracks that are available to anyone.

This also applies to the first few years of college.

Result? Everyone gets an amazing education, and you can't pay your way around it.

You might say that there is a risk that universities will simply select around it. In order to prevent that, universities may not use any criteria to select students from within the province, except a score, calculated from pre-university college education, that is a Z-score augmented by metrics from the performance of your classmates at standardized high school exams, deviation thereof, and a few more. The exception are programs like medicine and dentistry, where this score is used as the primary criteria but the interview and scores at ethical tests are also taken into account.

That way, there is simply no way to pay your way around it. Private high-schools are not competitive with the best public schools (which you can enter by exam or recommendation), purely private colleges and universities are even worse, and everyone ends up on a common track.

Result? In my Computer Science program, almost every minority is over-represented (the others are more commonly in Math or EEng), altough there is still a large majority of men.

It works pretty well. I would recommend it to you, but you'd probably need to sort out your incompetent-on-purpose government (from both parties). It would also require basically nationalizing every accredited university, but on the upside you'd have tuition costs of ~3000$ per year for every university.