Wouldn't a randomly moving platform with 4 gatling guns on there give full-sphere coverage and defense against passive weapons by the random movement? You have

Wouldn't a randomly moving platform with 4 gatling guns on there give full-sphere coverage and defense against passive weapons by the random movement? You have fuel issues, but that can be solved by rotating shifts, or (vulnerable) in-place refueling. If the Lagrange point is indeed unstable the random movement should be rather efficient to achieve. And kinetic weapons would need luck to hit you. For explosive weapons you might be able to rely on the gatling guns. It seems to me like the Lagrange points might be one of the few things in space you could occupy and deny an enemy. Perhaps LEO should added to that because it can be hit from the ground.