I would not use a pointed tool to push the rivets as this will expand their diameter. Instead take an 1/8 " nail and grind the front blunt. (Or buy a 1/8" punch) Then tap them gently through the holes. Usually when I drill them out with a 1/8′ drill bit I keep drilling until I am through the factory hole. In the picture I would try drifting them gently side to side to loosen them up and then tap them through the holes. I would not make new holes if possible as the factory seemed to use some accurate jigs to make the original holes and you will find them the same from car to car.

Dave Reina