I am thinking of education/admin track. Just that I am not sure if you need fcfp for these tracks in private sector.
Admin- perhaps MBA/mph more useful esp in private sector?
Education - can always email college or nus/ntu to apply as tutor. Also not sure if fcfp is needed.

Just thinking as you don't want to be doing degree for the sake of it. (You want to ensure that it is relevant and useful to your eventual end goal.)
My end goal is to take on some administrative responsibilities with a large gp group- be it something small like physician lead, pcn team lead, or more advanced roles like deputy/medical director in the medium-long term (if I am deemed capable enough of course) + perhaps do some teaching on the side (maybe with the college as a gdfm/mmed tutor or as a ntu/nus tutor for e.g)