I have used oversized balls in several different barrels - as a test. In my old .36 (360" bore - Hall Sharon buttoned barrel), back in the mid 70's, I had one heck of a smoothly funneled crown and used to load a .375" ball with a .022" denim patch. The rifle had a steel ram rod, 5/16" in diameter not 3/8". (edited-oops)
I checked the ball (in all my guns) just as you noted, galudwig , and what I had was a slightly more abrupt, shortened, but nicely radiused nose, with a somewhat elongated body with a perfectly symmetrical base with rifling marks all the way around, from grooves and lands. This is just as there always should be, undersized ball or oversized ball when using the correct patch.
It's the base of the projectile that MUST be PERFECT, not the nose, however the nose was also radiused, just like the base, but with minor damage, a slight shortening and with a ring from the outside edge of my starter's nose. No- I did not need a mallet or hammer.
It is vitally important that you hit the starter with your palm - ONCE - not twice or 18 times. Each time you hit the starter, you will do VERY minor damage - however, hitting more than once will give added damage - they add up. One blow - with anything , causes very little damage that does not seem to hurt accuracy, after all, it's the base that must be perfect as that is the last surface your LOAD has effect upon as it leaves the muzzle. Hitting the top of the ball with a flat object will cause more flattening than if using a cupped object. The commercial rod tips are very good, with their radiused cups. Duplicate those using files or tools on your lathe - poor man lathe or regular variety. If you don't have the expertise to make this item, purchase it from Track or other places and shorten them as needed for your short starter.