Enter on visa on entry 30 days, apply immediately for an education permit (takes 28 days) then apply for education visa, another 28 days. I would do it with the assistance of a good language school
I would do the 90 day irrespective of your visa extension. There are many experts on here but immigration is it’s own boss and difficult to negotiate with if they disagree 😂
It’s logical and sensible to finish a course of medical treatment rather than starting again. Immigration obviously saw it that way. They are often criticized but my experience has always been favorable also.