The simplest way to end government education is to convince them to charge tuition. Even if you could convince them to charge $50 a year, it would be enough. Once that boundary is broken, the tuition will go up and up and up until other alternatives are cheaper.
The problem now is that the education system has a near monopoly stranglehold because they have disconnected paying for it with attending it. Everyone is threatened to be forced out of their homes, at gunpoint, to pay for it and nobody has to pay to go.
The former won't stop if schools charge tuition. What I'm counting on here though is that government schools will be so magnificent at pissing away any new money they get, that they will always be hungry for more and more and more. Soon the tuition at public schools, that still receive like $15,000 per pupil per year in stolen money, will be so high that it will be cheaper to go elsewhere or home school.
If I were to campaign for this, anarchists would call me a statist. This is how narrow minded so many anarchists are. You can turn the system against itself. You can also infiltrate it.