I intend to make a bit of a career change so my knowledge lies elsewhere. I'd be curious if any decent MiM programs offer the possibility of applying without taking these tests.

If you are making a career change, you may have too much work experience for many MiMs. Although many schools have alternative tests (CAT, MAT, TAGE-MAGE etc) the top schools will want testing, either with their own tests or third-parties'.