I have just shipped my M-bags! I followed the advice that everyone gave. I wrapped all my books in plastic wrap, used the box within a box method, stuffed empty spaces with packaging peanuts and reinforced the outside of the boxes with packaging tape.
It took me forever, but hopefully everything will arrive in good condition. I work at a specialty food store (I shipped 168 gift boxes over Christmas!), so luckily I was still in packing mode! I'm counting my lucky stars that I was able to buy some good supplies at wholesale costs. I can't believe how expensive shipping supplies are in retail stores.
Anyways, I've been planning and thinking about this move for months, and it's so exciting to actually get things in motion. Thanks very much for the advice.