congrats on parallel processing - it's a great idea, but when all things work out, you have a predicament to solve, to be sure.
i would suggest thinking about why you want to get into MBB - do you want to get on the partner track, or do you have to have a lot of exit options in a few years. one additional value of an MBA is building out a network, one that you can potentially lean on when you're an EM/parter-track at MBB to drum up more business. so if you might want to be partner-track, it might be worthwhile deferring your McKinsey offer now to get an MBA. furthermore, chances are, if you have the right content knowledge, you can learn the case study method, and will be as strong a candidate for MBB after your MBA (though that may not entirely be true as i've never heard of the "expert" track before).
if you just want the MBB name on your resume (which is also totally fair) to open some short-term doors, as long as the broader industry doesn't underweight the "Expert" role, then by all means, feels like it might be the smart decision. though for what it's worth, if the "Expert" role is like a subject-matter expert, i would really do the due diligence as to whether it's a role that will open a lot of doors. being the same seniority as an EM doesn't give you the experience of an EM and doesn't value you as an EM.
good luck!