The concept of Kamma implies that information is stored in the mind
No, it does not! Information and storage are concepts. Not realities! The issue here is, we make the assumption that for causes to give an effect in the future, something needs to persist in the interim. When you commit a Kamma, the action is done and finished then and there. There's nothing stored. To give an analogy, take a stick and hold it at one end with your left hand and tap at the other end with your right. Your left hand will feel the vibration. But did any molecule travel from right to left? No! It's just that when the molecules at the place you tapped vibrate, the adjacent molecules start vibrating and then the ones next to them and so on. Then we make a concept out of it and call it a wave. But there's no wave in reality! The first molecule vibrated and stopped. It didn't go anywhere. Similarly, Kamma is also a concept given to describe a certain causes and effect process. There's nothing going from this life to the next or this moment to the next.