From Allocator to Public Investing

I'm currently on the allocator side (E&F), mainly doing manager selection, due diligence, and portfolio construction. I am considering an MBA to pivot into fundamental public-equity investing (LO or L/S).

A few questions:

1. Transferable skills: How relevant is allocator experience to fundamental investing? Would I essentially be starting from scratch?
2. Making the pivot: What would I need to demonstrate to convince employers I can succeed as a bottom-up investor? Are strong stock pitches enough?
3. MBA choice: CBS seems like the natural fit given its Value Investing Program, but how much does that actually matter? Would Wharton or H/S offer comparable opportunities despite having less structured investing curricula?

Would appreciate perspectives from anyone who's made a similar transition or recruits for fundamental investing roles.

Thanks!