The Southern HII Region Discovery Survey (SHRDS) is a 900hr Australia Telescope Compact Array 4-10GHz radio continuum and radio recombination line (RRL) survey of Galactic HII regions and infrared-identified HII region candidates in the southern sky. For this data release, we reprocess all previously published SHRDS data and include an additional ~450hr of observations. The search for new HII regions is now complete over the range 259{deg}<l<346{deg}, |b|<4{deg} for HII region candidates with predicted 6GHz continuum peak brightnesses >~30mJy/beam. We detect radio continuum emission toward 730 targets altogether including previously known nebulae and HII region candidates. By averaging ~18 RRL transitions, we detect RRL emission toward 206 previously known HII regions and 436 HII region candidates. Including the northern sky surveys, over the last decade the HII Region Discovery Surveys have more than doubled the number of known Galactic HII regions. The census of HII regions in the Wide-field Infrared Survey Explorer (WISE) Catalog of Galactic HII Regions is now complete for nebulae with 9 GHz continuum flux densities >~250mJy. We compare the RRL properties of the newly discovered SHRDS nebulae with those of all previously known HII regions. The median RRL FWHM line width of the entire WISE Catalog HII region population is 23.9km/s and is consistent between Galactic quadrants. The observed Galactic longitude-velocity asymmetry in the population of HII regions probably reflects underlying spiral structure in the Milky Way.