Does point 9.1.b) basically say that I can leave whenever (except in those cases mentioned at 9.1.c) ) as long as I notify them 30 days in advance?
Yes. The clause conclusively entitles you as occupant to terminate the license prior to May 2020 (subject to 9.1b and .c).
The interpretation that the "31 May 2020" term is in addition to the requirement of a ...
You could be right
Of course, so could they
This is a really good example of a really poorly drafted clause. It could mean what you think it means, it could also mean that the 31 May 2020 is the earliest date for termination and one of the other subclauses must be followed.
You can't "make the landlord understand"; you can only explain your ...