National Association of Independent Schools (NAIS), NAIS Career Center|Find Your Career Here
Job board for the national association of independent schools. It's a good resource as the school year nears next year to look for things.
I'd strongly suggest considering using that and sites like Indeed to find work you'd find suitable. At this point, you're going to find yourself increasingly competing with people who have work experience AND the degree you have.
You need some formal experience outside adjuncting to really make yourself marketable. I think going to private HS route is smart because they're likely to hire you, you don't need to be certified and your college teaching experience will make you attractive.
But you need to sort of find a gig that works, because the PhD route makes sense somewhat, but with more and more people finding a harder time getting work with their doctorates, you're going to need to be creative or strategic to use it or else you'll be overeducated, underemployed and limited in the relationships outside of higher ed that you can use.
Just .02. Good luck on the GRE.