I used to have the exact same issue, try to clean up as much of the epoxy while its wet. Small c-clamps work well for the rounded edge of the overlay, a washer or quarter will keep the rounded edge down nice and tight.
I have the Dremel Stylus, its the small gun shaped one, excellent control, like holding a pen and the 240 grit is pretty forgiving.
I cant imagine doing tips without it.
When all else fails, a flat finish is your very, very best friend.