That is going to be tricky since the menu is wrapped in the <ul>. How about creating 1 item menus in the Menu manager and then putting them each in separate module positions? See how that goes.
Are you using a solid color background? You could maybe just make the right border thicker and make it the same color as the background. There is the "first:child" and "last:child" stuff too that you can add css for if you need to add a left border to the first, or no border to the last or something.