Thank you for all the responses and for all the interesting insight! The date of the home run was July 30th, 1990 Padres vs Braves. The ball does have the Haiti stamp and definitely looks like a game used ball. I am going to try and attach a few pictures of the ball. I guess my only concern is that maybe Jack grabbed another ball that he had and said it was his 300th HR, whether intentional or not. There is writing on the ball in ink that looks pretty old that says 300th HR and the date and who he hit it off. He then signed "My 300th" when he sold it in 2007.
Another forum member sent me a private message and said in his experience in the industry often times balls from previous years are used even if the commissioner has changed, that especially back in 1990 they would never just throw away good balls. Also the fact that Giamatti died suddenly would make it even more likely they would still be using his stamped ball in 1990.
All in all I am leaning towards this being the actual ball, just funny how it just had to have the Giamatti stamp which would naturally make me question its authenticity.
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