The panzerschiffe had 80 mm belts and 45 mm decks. The Indianapolis carried the pre-war marks of US 8" guns in the early mounts, so they were never able to use the super-heavy AP shells, kind of like Colorado's 16" guns being limited to the 2,200 lbs US AP. The Indianapolis's shells were 260 lbs for AP, HC, and Common. Even with the lighter shells, the Indianapolis would be able to penetrate AGS's deck beyond 18,000 yards and penetrate AGS's belt up to about 27,000 yards, so AGS would not have had an immune zone. The Brooklyn's 6"/47 Mk. 16 guns were able to handle the 6" super-heavy AP, so they would have been firing 130 lbs shells instead of the typical 100 lbs shells that guns in the 150 - 155 mm range typically fire. Navweaps doesn't have penetration curves for these guns, but it does say that the super-heavy "projectiles had almost double the penetration performance when compared against the older 6"/53 (15.2 cm) AP projectiles used for the Omaha class (CL-4) light cruisers." Based on this, I would estimate a possible immune zone for AGS in the range of 17k to 18k yards, if one even exists. The Brooklyns would be able to get belt penetrations at shorter ranges and deck penetrations at longer ranges.