The easiest solution is to change your sight picture. It is more accurate to have the point of intended impact be the very top of the bead, rather than cover the target with the bead. When you cover the target, you are really obscuring your intended target.

I shoot open sights as far as 200 yards as described, if I were to cover the target with the bead I would not see my target or anything around it. Instead I have a nice and precise point of aim given by the point at the top of the globe -- which is why I use globe fronts and not blades.

MTA: This is consistent with picking a particular visible point on the deer to aim at, rather than the whole chest/deer which is about the best you can hope for when you can't see your target behind the sight.