Solar-pumped solid-state lasers are promising for renewable extreme-temperature material processing. Here, we report a significant improvement in solar laser collection efficiency by pumping the most widely used Nd:YAG single-crystal rod through a heliostat-parabolic mirror system. A conical-shaped fused silica light guide with 3D-CPC output end is used to both transmit and compress the concentrated solar radiation from the focal zone of a 2 m diameter parabolic mirror to a 5 mm diameter Nd:YAG rod within a conical pump cavity, which enables multi-pass pumping through the laser rod. 40 W cw laser power is measured, corresponding to 13.9 W m-2 record-high collection efficiency for the solar laser pumped through a heliostat-parabolic mirror system. 2.9% slope efficiency is fitted, corresponding to 132% enhancement over that of our previous pumping scheme. A 209% reduction in threshold pump power is also registered.