How do you think it would be best to address the students that are always looking to put in the least effort and only approach an assignment in the 11th hour?

I can't see a time when multiple choice questions are not going to be useful. I think that we will have a better opportunity to ask the questions that pry into the level of understanding that the student possesses. I think that well constructed questions can still be used in multiple choice format and could also allow the student the opportunity to defend their thinking with a short response.