I saw a lady do a different ( to me) binding. Sorry I didn't catch the name of the tecq. Here what she did & I can see this work for you. She sewed on her binding from corner to corner. When she started she pressed the edge of her binding about 1/2 inch, then folded her binding, to make a double fold. Just before she got to the corner she cut the binding. Then folded her edge under. At this point you would change your color of binding. Hopefully someone knows what this style is called. I'm not to good at explaining what i mean. But I know this would work for you.