Assigning multiple choice exercises as homework

I'm in the process of writing nightly problem sets for my new Honors Physics I course.  These are essentially the same problems that I used for AP Physics B; however, I'm rewriting the problems to include more verbal explanations, and so that they're typeset on the front and back of a single page. 

Most of my homework assignments are simply rewrites of textbook end-of-chapter problems to make them AP style, and to explicitly demand verbal responses.  Occasionally, though, I want students to work through a set of multiple choice questions.  I *could* give these as a quiz in class; but to make the quiz worthwhile, I'd have to go over the quiz in detail.  I usually want to use class time for other purposes.  How can I usefully assign multiple choice problems for homework?

The issues are probably obvious... It's too easy for students merely to copy the (presumably) correct answer from friends without thinking through the answer thoroughly.  The simplest response is to require students to justify every answer with verbal reasoning.  I do this occasionally... but I don't want to assign more than three or four multiple choice per night in this manner.  How can I get folks to work through a longer set?

Once in a while, I'll pass out a 20-question-or-so multiple choice exercise and a scantron form.  I require each student to answer each question on the scantron by himself, without collaboration.  (You can enforce this either with an honor pledge, if you can trust it, or by using 20 minutes of class time.)

Next, I require each student to check his answers with classmates.  Everyone's final answers go on the reverse side of my two-sided scantrons.  I only grade the final answers.  The trick is, if a student changes his answer based on collaboration, he must write a verbal justification.

Grading is easy, since I can scan the scantrons, and spot-check the justifications.  The assignment is not excessively long, because students only have to write justifications for the ones they missed initially, and since the discussions with classmates when they are finding out which ones they missed will make justifications quick.

Sometimes I'll ratchet up the grade incentive for useful collaboration.  I'll take off one point for the first wrong answer, but two MORE points for the second wrong answer, and three more for the third... someone who gets 16 of 20 right would thus earn a 50%.  This grading system has led to wonderful physics arguments within the class, which of course is the whole point of any homework assignment.