Another assumption here is that the radial momentum which you put on the counterweight in order to accelerate the payload is paid back upon braking. The momentum you put on the counterweight in order to *lift* it against gravity is, if I see it correctly, a function of the time you take to lift the object, and one should be able to reduce it by lifting quickly. But this is a bit messy and one possibly needs to do the full calculation after all to understand this.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition
