To answer your questions:
(1) A strong GMAT (700+) will help with a low GPA. As for work experience it is the quality that counts, but no matter how amazing you may think you are, you've only been working for about a year now (yes, 2 years at matriculation but you only have a year worth of experience to talk about) - that will be an issue not just for part-time but full-time programs as well.
(2) Being sponsored and the brand of your employer helps a little, but it's not a game changer or anything. It still comes down to your overall caliber as an individual.
(3) Kellogg is a maybe. As for HBS, you seem like a solid to strong professional, but there's enough folks out there that have stronger resumes than you who will therefore be ahead in line (before you ask, "how can I be more competitive then?" - be effin' exceptional in the way *you* know how - in the realm of being an overachiever, no one tells Michael Phelps how to be a "good enough swimmer" -- in other words, it's not about being "competitive enough" but being the most accomplished person that you can be regardless -- and whether that is "good enough" or not for HBS is not in your control anymore than whether someone is "good enough" to make it to the NFL, or "good enough" to have a successful business, or whatever; you do the best you can in whatever avenue or thing that you enjoy doing, and let the chips fall where they may).
(4) Focus on Tuck, Kellogg, Michigan, Duke, Darden in 2-3 years' time. You should be competitive for these schools if you have solid work experience at a good firm and a competitive GMAT score.
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