Balistrol is good because it is base in PH level by design. It neutralizes the acids that lead to corrosion.
Salts also help start rust, and a big source of salts is soap. Simple green does not have salts, so it is a good choice for a cleaner.
Once a barrel is pitted, then the corrosives hide in those nooks and crannies. At that point it will be very tough to clean properly.
