I usually use material that is thin enough that it bends into the limb's curve during glue up. These pieces are usually core-tuff of whatever color best suits the bow, and then hardwood on top. I either sand the gluing surface of the wood with rough grit sandpaper or groove it with a toothing plane blade, then use Smooth On epoxy, and set a work light next to it for warmth while the glue cures.
Replacing the overlays so that the tip remains sound is a good idea. If it is rough, chipped, or separating at all, and can continue to get worse and even lead toward a delamination or other failure.