Elite prep schools are tough to crack, because sometimes you are competing with very experienced, high-quality, award winning public school teachers who are ready to make a lateral move to an elite private. Hard to compete with them.

If you want to kill a year or two, it's much easier to get work in an American school abroad, which always have a mix of expat brats and rich elite locals. The pay and housing arrangements are often surprisingly attractive because they find it hard to get people to move (there is a huge amount of turnover at these places). Plus you might spend a year or two in some fascinating city abroad.

Either way, if you want to come back to academia, you'll have some explaining to do to that future search committee.

Less prestigious HS jobs are less competitive, but more likely to require teaching credentials, which would require more years of eye-bleedingly stupid Ed. dept coursework.

Either way, life would be hell on earth. HS students are horrible people, and you have to spend your whole day with them, five days a week, rather than 5-10 hours a week in college. It's not a good life.