Where I live there's no requirement that schools accommodate gifted students, so it's all about trying to persuade the school that what you want is a good idea and not too hard for them.
My first step is always trying to establish credibility so they know I'm not just a pushy parent. I know some people do this with testing. I've taken the approach of letting them get to see my kids in class and spending a lot of time in the school volunteering.
During a school year I start with the classroom teacher. Teachers are happy to have easy problems, so if you explain what you think the needs are, and show them materials that you think solve the problem, they can be happy with this. It's easier to get an accommodation that your child can work on their own during math time than to get them to actively teach something, but I'm always happy if I improve on the status quo. If your class has kids who could form a math group and work on the book together that's obviously better. Having a group of parents supporting each other is also more powerful.
If you're trying to set something up in advance for next year, you do have to go through the principal. Your principal anecdote sounds promising. If she's personally a math teacher, then that's even better and encouraging her read to through the book could be a good method of approach.
Others here probably have more experience than I do.
