A stock 5.9 is NOT (factory) internally balanced!!! Are you saying this engine had previously been "built" and internally balanced by a machine shop? In either case, tho, changing ANY weight will change balane, AKA changing rods or pistons
On the other hand just how wild is this thing? Many of those pistons may be designed for "stock like replacement" even though they are not necessarily same as factory weight. If this is a 6K/ under RPM street car you may be worrying about nothing.