I have good luck using double fold continuous binding but that is not the only way you can finish your quilt. Some people like to fold the extra back fabric over to the front and stitch it as binding. The only problem I can see with binding each side separately is you will still have to fold and stitch the corners some how. Have you thought about rounding your corners? I have on occasion used straight grain binding on most of the quilt but sewed on a 10 inch section of bias binding to go around each rounded corner. It turned out great.