I am an elementary school teacher finishing up my M.Ed. My degree will be in (project) Management and Innovation. Rather than applying this to education, I was actually starting to consider the possibility of leaving the classroom and going into Project Management. I did a job search and saw that there ARE openings for PMs, but most say that they want 5-10 years experience. I did see one that was an education-related PM position that said they’d train newbies, but is that going to be hard to find again?

Suggest you look at a project administrator role to start with. While it is mainly clerical, it does expose you to project management and provides inside opportunities to start managing small projects. Also look at roles within a program or project office. These can also put you in the right place to get into project management. Typically you will start out either doing very small projects, or assisting project managers. As the experience builds, you can move into more mainstream project management.
Neville Turbit