I'm having the same problem. When I got to the border, I needed to cut a little too close to the points when I squared off the top. Now that I am sewing my border on, I'm losing a few of my points. For me, I decided to try to do some surgery to the top and see if I can take things in slightly to re-establish the points. I don't like doing it, because it makes the edge less straight, which will lead to re-squaring and possibly loosing even more points. I've only done about 3 or 4 of the points so far and I might just leave it there, as it might get too wonky if I continue. I never thought of appliquéing anything over them. I'm not sure I'd do that on my quilt, but maybe on one where the stars become part of the design.
~ C