We present the spectroscopic discovery of 69 quasars at 5.8<z<7.0, drawn from the Hyper Suprime-Cam (HSC) Subaru Strategic Program (SSP) imaging survey data. This is the 16th publication from the Subaru High-z Exploration of Low-Luminosity Quasars (SHELLQs) project, and it completes identification of all but the faintest candidates (i.e., i-band dropouts with z_AB_<24 and y-band detections, and z-band dropouts with y_AB_0.1 in the HSC-SSP third public data release (PDR3). The sample reported here also includes three quasars with P_Q_^B^<0.1 at z~6.6, which we selected in an effort to completely cover the reddest point sources with simple color cuts. The number of high-z quasars discovered in SHELLQs has now grown to 162, including 23 type II quasar candidates. This paper also presents identification of seven galaxies at 5.6<z5.6. This demonstrates that the algorithm has very high efficiency, even though we are probing an unprecedentedly low luminosity population down to M_1450_~-21mag.