Of course it's impossible to evaluate shot string by shooting at a target that's not moving. You need to get your wife to tow a target sled behind the family vehicle, as Bob Brister did. Then string will show up . . . although probably not a lot of it at 30 yards or closer. And if it does, there are a lot of factors at play: Choke, hardness of shot, plastic wad vs fiber, etc.
I'm not much for the "square load" thing either. If the 2" 12 has an advantage, I expect it stems at least in part from having a very short shot column . . . although that shot column is no shorter than it would be in a 2 1/2" or 2 3/4" 12ga shell, assuming they're all shooting the same payload.
