"Bureaucrats tend to be less than enthusiastic about adding work. "
Baloney. It just gives them more of an excuse to hire more people and expand their budgets. And if it gets too onerous to review curricula then they will just legislate only certain ones are approved.
You are a very trusting soul when it comes to bureaucrats.
"I'm sure you've seen a few of each, if you've moved in those circles for any length of time."
Yep. Overall, though, the stats show that they do better than public schools. For now that should give guidance on how to proceed.
Ever work in an over-worked bureaucracy? Things just don't work that way. Bureaucracies will tend to focus only on the egregious problems, and tend to do a cursory job otherwise. Furthermore, it's trivial to establish a deferential standard of review in the procedures. Any second-year law student can do it.
Overall, though, the stats show that they do better than public schools. For now that should give guidance on how to proceed.
The way you cite those statistics is fallacious. Statistical averages tell us just that - the average. It counter-balances the low-performers with the high-performers. The distribution curve of the scores almost certainly shows that there are high-performers that would do well in any half-way decent school, middle-level performers who are thriving under individualized attention, and low-end performers who may struggle in any environment, or whose parents have no business homeschooling. An average gives no information about how many fall in each category.
On the other hand, the stats do tell us one thing - homeschooling does work and should be a viable option for some. Anything beyond that is conjecture.