The Ministry of Education does have a list of accredited universities which it checks against when the cram school manager sends a copy of the teacher’s degree certificate when applying for a work visa. My guess is that they don’t make the list publicly available for diplomatic reasons and/or they couldn’t give a toss about making life easier for foreign cram school teachers. The onus is therefore on the teacher to check that his university is MOE accredited before coming to Taiwan.
I stongly advise you to contact the MOE directly to check that your university is accepted before coming to Taiwan.