We report the successful molecular-beam epitaxial growth of 10 stacked layers of GaSb/GaAs quantum rings using a new procedure. Exact control of the arsenic flux during capping helps to reduce the strong group-V As-Sb exchange reactions, enabling the rings to be capped at the same growth temperature (480 degrees C) without dissolution. X-ray diffraction and transmission electron microscopy indicate excellent structural quality and uniformity with no threading dislocations. This is due to the reduction in the average strain through the quantum-ring formation. The total ring density in the stacks is 1 x 10(11) cm(-2). An unusually long-wavelength quantum-ring photoluminescence peak of 1.3 mu m is observed at low temperature, which is attributed to a reduction in the quantum-ring charging due to lower unintentional p-doping in the GaAs cap layer. The impact that this effect will have on future device designs in solar cells and lasers is also discussed.