Firstly, Columbia is definitely a re applicant friendly school. Why do you say they are not? 10% of applicants at columbia are re applicants, and 20% of them make it - higher than the overall selectivity of 15-16% (Source: Businessweek, stats from last year). I am not sure about Sloan. Kellogg is definitely reapp friendly and probably the other schools you mention. The only schools I know of which are perceived to be reapplicant unfriendly are HBS and INSEAD.

To get into a Columbia as a reapplicant, more than one of the following should definitely help (not in order of importance):
1. Very good improvement in your GMAT score - assuming you are below 700, taking it above Columbia's GMAT average of 710-720
2. Strong career progression at work - promotions, additional responsibilities, large team. Changing jobs from a smaller company to a bigger company, OR the other way round with a highly exciting role in the smaller company
3. Great recommendations - last time you could have had a weak/bad recommendation, maybe even lukewarm. You'll probably want to select your recommenders much more carefully and monitor their enthusiasm much more closely
4. Excellent essays - hit them out of the park! Columbia of course doesnt give you enough room to do this, requiring only one additional essay from a reapplicant. But you can shine through if your overall profile captures the above + you write a fantastic essay

Hope this helps.
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They don't compare your previous application from the newer one, unlike Berkeley.