Maybe I haven't understood your explanation!
Seemes to me that if A/S and PWR are constant, the lighter aircraft will not descend as quickly as a heavy.
Ex.
140 tons will have a gradient of 1.5% gradient and at 220 tons, A/C will have a 3% gradient. (Again assuming the power and A/S remains constant)
In effect, whether we are heavy or light, we always descend at idle pwr settings. In this case gravity has the effect of increasing the gradient and hence, the airspeed. The heavy aircraft will descend faster but the speed will increase faster to Vmo. Therefore the rate of descent must be reduced, increasing the TOTAL distance required. The light aircraft can keep the higher rate of descent and not approach the Vmo as fast.