So we have one SM3 Missile with a 28 lb odd (14kg) solid shot kinetic warhead which is designed to strike and punch neat round holes in compact precision assembled nuclear warhead of say 2 foot diameter at 100 miles up travelling at some 7000 mph and shatter the re entry heat shield at the same time !
Thus hitting such a larger object like the Lacrosse Satellite is never a problem !
Now we have a a very large 2300kg cylinder some 10 foot in diameter and 20 foot long rotating in three dimensions due to a combination of very thin air drag , solar winds and the earth's gravity well and magnetic fields acting upon the heavier end and the deployed radar array acting a bit like a friction aero brake of sorts ! So in the last two years it will not only be rotating but also tumbling/twisting end over end as it is free to move in three dimensions ! Remember all Newton's laws of motion also apply too ! So essentially a slingshot stone will have minimal effect on a travelling boulder , and a shot gun even less so as the shrapnel will rip little holes through the non resistant thin exterior fabric !
It is a given to save weight the exterior will be made of a combination of ultra thin aluminium and gold foil with a sections covered in fragile ultra light weight solar cells , so the the terminal warhead will literally punch a number of fist size holes straight through from one side to the other at random which may or may not hit the hydrazine fuel tanks within the satellites body dependent on the time of impact and relative to the bodies motion in three dimensions !
However one can not ignore the fact that current Aegis Cruisers with have a finite limit on the number of silo launched SM3's and after x number of rounds the gun is empty and have a limited firing arc to intercept window given the terminal velocity of the satellite and the fixed range of the missile , it's time to terminal velocity and fixed maximum range and time to fire from target acquisition on board ships computers calculating range and shoot numbers before it drops below the horizon very quickly as everything is relative !
As Paris would say "Duck and Cover , Nuts to the moron that thought this one up !"