progressing from high school teaching into academia
If you are near completing your PhD, then I assume you also have some papers coming out soon. If not, then your dissertation will probably be worth 3 papers, so I wouldn't worry too much about that part.

Conveying information to an audience with varied skills and backgrounds is always a valuable thing in academia. Whether in written manuscripts or conference presentations, this is usually the problem to be solved. My advisor was fond of constructing lectures, no matter the audience, as if they were to be given to college freshmen. I'd say a lot of freshmen are not too different from high school students.

A successful PhD defense signifies that you have the ability to do novel work in your field, but your teaching skills will enable you to tell others about it.