I had the same problem and took off the top lip of my big adult tubs. This made the plastic way too flexible and I trashed it because I was afraid my big girls would push out. My tubs are also in sideways so it will probably not be a problem if they are in front to back and its a smaller bin.

Just a word of warning. I did it with the dremel and it was a PITA! This is the DIY shelf rack. I just need to be extra sweet to my fiance so he will adjust the shelf!