OP, your chances of successfully transferring are based not on what you seek but on what the proposed colleges believe you will contribute to their campus. The competitive schools do not need to accept transfers and generally do so when it will benefit them. If you can make a convincing case that you need to pursue an education certification unavailable at Williams but possible at your new school and are eager to get involved in related activities, that would help. Do not assume that the student body at any of your proposed schools varies materially from that at Williams-the degree of extracurriculars and FGLI support there is not likely to be exceeded elsewhere and you would likely need a state school to obtain great SES diversity.