It is a good time to think about it but I can tell you that things will get much more real when you have the admits and decisions will be on the line along with huge amounts of money.
You are asking great questions - it is pretty much all recruiting on your own, known as "off-campus". Translation: you will have to do the networking and bugging people on your own. The cool part is that the alums are VERY responsive and very supportive. I would highly recommend reaching out to students at the Sloan Fellows and MSx to get a sense of the programs, recruiting, and options.
My understanding is that Sloan is much more international, I think 70% international If I am not mistaken (I may be) whereas MSx is more US domestic applicants, which helps as your network is more local in the US vs. global (unless you want a global one of course). Transitioning at this stage in the career is tricky, esp if you don't have the work experience in the field but it is possible. You want to talk to the current students to get a sense of the effort required and also what you can do now to ease your transition...