I want to cut the binding 3″ wide, so that it will show up more. I read somewhere that the batting should fill the width of the binding, and that sounds good to me. I’m thinking that the easiest way to do that is to just do a 1/2 inch seam instead of 1/4 inch when attaching the binding. This does narrow the border by 1/4″ but I made the border bigger than I needed anyway. What do you think of the above method?

You can do your binding as you suggested for sure. The other method some people like to use is to cut their binding 3″ and sew it on with a 1/4″ seam allowance, stuff extra batting along the edge of the binding, fold over and stitch down. It makes a puffier more pronounced binding.