Hi godspeed,
Thanks for writing and sharing these details. One of the biggest challenges I think you'll face is explaining further why you want to get an MBA since you already have similar post-grad experience. Beyond just saying you want to move into General Management, go further by saying why an additional degree will allow you to achieve things that you can't now.
I don't have a ton of familiarity with the programs you list as most of my expertise is in traditional two-year programs. Given, that Kellogg might be a bit of a reach and your challenge with the LBS MBA will be proving the point I made in the above paragraph.
As for recommendations, you want them to be all professional if possible, not academic.
Best of luck,
Daniel Richards
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