It sounds like you maybe stretched the bias edges when putting the binding on. You can re-do the binding and ease the bias edges towards the needle to hopefully bring in the extra. OR you can take the original binding off, stitch a row of large gather stitches on each of the 8 sides. Gently pull the top thread to bring in the fullness in until the edges lay flat again and re-apply the binding.
OR you can try Charisma's Quick machine binding with flange. I like to use Charisma's binding on small wallhangings and toppers that I want to lay really flat. The extra fabric seems to add an extra stiffness to the binding. Here is a picture of the Oak Leaf one I did.