I like my binding full, too. I cut the strips 2-1/2 inches and fold in half. Then I align the edge of the binding to the edge of my quilt and use the regular sewing foot...not the 1/4" foot.
Using the regular sewing foot makes it the perfect width to fill the binding. It's closer to 3/8" than 1/4" and looks good. When I fold it over to handstitch and finish, it's just perfect.