Did you put some type of cushioning material in the puller to help prevent the bullets from deforming? Even though they look good, the tip could possibly be bent, although I have been told that the bent tip won't affect accuracy. I have reloaded pulled bullets in the past, but don't use them on my elk hunt. I use them for practice, sight-in, etc but not for the 'once in a lifetime' shot. With the price of bullets these days, and the lack of availability I certainly wouldn't trash them, but sounds like you haven't done that since you reloaded them.
For deer, coyote, etc hunting I think I would use them, just not for my elk hunt.