I just did this (switched schools from Korat to Chiang Mai). Immigration would not cancel my work permit and visa ahead of time, so the whole process for me was like this:

-cancel work permit (morning)

-cancel visa (afternoon)

-drive to Cambodia and exit and re-enter with a tourist visa (same day, to avoid overstays)

-move to Chiang Mai and get the paperwork from the new school

-fly out of country to apply for non-B and come back in with the

non-B visa.

You might be able to eliminate one trip by having all your paperwork from the new school and applying for the evisa while in Cambodia or whatever country you can get to same day.

It was a headache. So, I hope you find a better way!