That’s most of what’s required for a damaged goods on arrival claim, except the condition of the unopened box needs to be shown as well. So what you already do should be good enough.
I still have reservations about the batteries. When you send them back you are responsible for assuring the safe shipping status. We don’t know what they will be subjected to with package handling but we should assume the handling will be rough. As you’ve indicated the batteries are not in an ideal state, how much risk are you willing to assume?