Appreciate and respect that. But you could be working in your desired field in a year or two, vs. the MUCH longer way around the mountain with a doctorate…
Take a look at some of the big foundations which work in educational innovation/improved access/DEI; a couple of think tanks doing criminal justice reform, sentencing disparities/holistic defense, organizations like TFA, Kipp, Baltimore Corps which have their own metric gathering/analysis teams. If virtually everyone has a doctorate- then continue on the path you’re on. But if many/most have a different path, you may want to consider that.
I think folks at the World Bank, UN, who do this kind of work are PhD’s. But there’s a whole world of actual reformers who fund, manage, launch, create disruptive social sector organizations and I suspect they are not dominated by PhD’s. And the analytical/research work- seems like a quickie program would teach you what you need to know to pivot.
If your interests extend into public health- some great, not too long programs in that field!