I am also interested in sharing the learning of Greek with my daughter, so I noted this link recently posted on this site under another topic:
I'm not experienced enough to know if the dialect is Homeric.
I'm sorry that I don't have an answer to the original question about classical education and resources for teaching Greek to a Math-oriented child. While I do think it can be useful to look at the educational methods of the past, in my particular case, as a parent, I am happy with the methods of today, so I have not had any motivation to investigate alternatives.
I have noticed that often a talent for Math and a talent for (and interest in) Linguistics go together. That might be an avenue to explore. A language is based on a system of rules and patterns, and I think that appeals to Math-oriented people.