I've addressed binding sleeve hems before, but have since been doing it a bit differently.  Too many seams in one place adds a lot of bulk, so I've changed my seam in the binding to a bias seam.  Measure the opening to determine the length of binding needed.  Cut one end of a strip on a 45 degree angle, then measure out the opening length PLUS 3/4" and cut the end the same way as the first.  Sew the ends with a 1/4" seam, then attach to the garment.