Am I getting too jaded about this, or are your official ‘solid reasons’ not the actual main reason for transferring?
Did you apply to any of the schools you are asking about (NU, Vandy, ND, Brown, Columbia, Penn) the first time around?
Vandy and ND have reps for being comparatively accessible for transfers; Columbia does not- and it is harder logistically b/c of the Core.
Not your question, but are you sure that both Brown and ND would suit you?