I have a background in education (was a high school teacher) and in my pedagogy classes it was emphasized time and time again that a well-written multiple choice exam is a good way to evaluate what your students have learned. Of course they are not (and should not) be the only way students are evaluated, but they definitely have a place. Why are you against them? A horribly written multiple choice test can definitely make you want to pull your hair out, as can those stupid a) I, II, and III, b) I, II, IV, c) II and IV, etc questions (they not so much test what you know...more like they test your patience).
Just wondering what your main gripe about multiple choice is...to me whether a class is upper or lower division doesn't automatically change what the evaluation scheme for the class should be. Interested to hear your reasoning behind it, that's all...we all are entitled to our own opinions🙂 I just happen to like multiple choice personally, so I'm going to defend my homie!