You can stitch the binding on using a 3/8" seam allowance.
I sew binding onto the back using 3/8" seam then turn over to front and stitch down. I can see where the stitches are on the front and control the corner turns easier.
Or cut the binding smaller as mentioned above.
I made some scrap samples of both to determine which method worked for me. Generally, I don't iron the binding in half before stitching either. The binding edge lays flatter without the ironed edge. A light press to flatten the binding edge afterwards and it's all good.