I don't think you cut it wide enough to do what you are trying to do If you want the binding to actually show 1 1/4" on the front and only 1/4 inch on the back.
I would sew a very thin border on with the same fabric as the binding is going to be to create that effect then bind like normal.
You'll have to rip the binding off that you so carefully put on last night but I think it will work fine to add a thin border. You might want to use a walking foot and loosen the pressure on the presser foot it possible to keep from scrunching up the sandwich.