Agree that a cheap duffle with pack sounds like a good option if you have to check the pack. I'm in the outdoors equipment business, and I've never heard of packing a pack into a box with styrofoam for travel. I don't agree with the "disposable luggage" concept. We have softer (zippered) luggage that we've been flying with for dive trips for ten years now. It's not el cheapo stuff from a box store, but its not high end either. We got it at Macys for 70% off some years ago. It's held up just fine.

For OP, if you are going just for a week, why not pick up some sort of bag that you CAN use as a carry on? Not having to check stuff is really really nice.