Instead of theorizing, just call and ask why they haven't responded. If the answer is "Because we're snowed under", well, there you go. And now they know that you really give a shit because you're badgering them for a response. They get a lot of form letters but very few people follow up. That immediately ups the seriousness in their minds.

Be unreasonable if you have to be. I don't mean impolite. Be nice to the human being on the other end of the line. But be demanding. Your MP works for you. Make them work.