First remove the top flaps with your handy dandy razor blade cutter. Second, use some spare contact paper and cover the boxes. I just covered the sides and the top inside edge of the box. The advantage of the zebra stripe print is that it doesn't show the wrinkles very well.
Here's a quick visual for you:
You can't even see most of the vinyl in the before picture because it was being stored in my dresser. Now I can easily see what vinyl I have and know better when to reorder. And I can actually use the copy feature on the printer without moving tons of stuff. :)
The liquor store box solution might not work if you have lots of heavy rolls of vinyl, but it works perfectly for me.