Do the same thing, but instead of LEO, throw your BBs into a retrograde orbit at geosynchronous altitude. They will hit comsats head-on, and the volume to fill with shrapnel is manageable since all the GEO satellites are in essentially the same orbit.

In fact, you don't even need to fill a volume, only a plane:

Create a disc-shaped cloud of BBs that is say 100 miles in radius and a mile thick, centered around an ideal GEO orbit. Maybe it needs to be 200 or 500 in radius, but still something relatively small.

Every 12 hours, every single comsat will pass through that cloud at a relative velocity of 11,000 miles/hour. It shouldn't take too many days before they are all dead. And at those altitudes, that cloud should last for quite some time before the orbits decay.

Of course, this requires more capable launch technology than LEO, but on the other hand, probably requires a much smaller number of launches.

There were actually some worries about the Soviets doing this in case of war. They made much less use of GEO -- their birds tended to be in Molniya orbits -- and so taking it down would have been a much greater relative loss to the US and NATO.