Do you have a general set of shotgun dynamic measurements that you like?
If there is a number you are working toward, you can do that on paper and then add a set of weights to accomplish it.
If you are doing it iteratively, I have seen someone take a 2 ounce sinker, thread a 3/8 inch hole through it and use a piece of threaded rod to move the weight for and aft within the butt stock.
I don’t find shotguns balanced exactly on the hinge pin to be satisfying for my shooting.
An inch or two ahead of it seems to be a much steadier configuration for me
