What a fascinating set of ideas. Now this is only theory but it sounds logical to me.
Your column of shot is pushed out of the barrel by the wad. The leading pellets are pushed by the ones behind them. As the pellets are spheres there must be a 'snooker ball' effect with many of the second row of pellets pushing the ones in front out at a slight angle. The third row will in turn push the row in front outwards if they are slightly inside of them and so on. The pellets not towards the outside will probably have 3 pellets pushing it equally from behind so should carry on in a fairly straight line - which would explain central density and why for a given load 12 bores tend to pattern better than 20 or 28 bores.
No doubt factors such as air flow through the shot mass and deformed pellets will also have an effect. The pellets on the outside of the column will be hitting still air on the outside while the ones progressively nearer the centre will be in a moving column of air with equal forces all around its sides.
I did read somewhere that the elasticity of the binding agent of tungsten matrix shot caused it to 'spring' apart like compressed golf balls but not too sure how one would go about devising an experiment to test this theory. If it were true then must substances have some elasticity - lead less than most - it doesn't bounce much when dropped but even a tiny amount may have an effect.
Just a few thoughts with absolutely no proof!!
Blow them all out of the water if you like - I have a tough skin!!
John