There is no job worth having for which you will not need some degree of re-training and upskilling. You have virtually no chance, even with that sneaky Masters degree you ve been doing, of simply taking over a different kind of organisation. What I am trying to say is that this project will demand every ounce of your professionalism and that the rewards you envisage are some way down the tunnel. Moving out of teaching is much harder than moving in. One last thing to get clear about is that nobody will help you with this move.
Recruitment agencies exist only to garner fees from employers.
The local careers service will not be experienced in this kind of stuff because there are no clear pathways laid out. If it was easy, everyone would do it. Because it is not easy, you will grow and mature and impress potential employers by becoming well-informed and employable in their eyes.