I believe that Vanderbilt is quite diverse and each year there is a very active Vandy transfer thread here on College Confidential. You may want to check it out and ask your question there. Good luck!
Edit: what you may not be enjoying at WashU could be the large lecture halls. Compare sizes of classes at your target schools. Perhaps you should transfer to a LAC where classes should be smaller and you should have more access to professors during office hours. Consider Middlebury College along with the other NESCAC schools you listed. Reach out to them as they have February admissions, though not sure about for transfers and the timing of same.