I have talked to my local ASA guy and he said that both teams should supply their 2 game balls to the umpire to start the game. From there, either team may replace those provided they do so at the beginning of their 1/2 inning on offense. The balls then must go thru the normal rotation system. This applies to any inning, even the bottom of the 7th and is fair to both teams.
So, in the end, since the parks supplied crappy used balls for years, we had to go out and buy better and better bats to compensate. This is a step in reversing that trend!! (said tongue in cheek)