The Southern H ii Region Discovery Survey (SHRDS) is a 900 hr Australia Telescope Compact Array 4-10 GHz radio continuum and radio recombination line (RRL) survey of Galactic H ii regions and infrared-identified H ii region candidates in the southern sky. For this data release, we reprocess all previously published SHRDS data and include an additional ∼450 hr of observations. The search for new H ii regions is now complete over the range 259° < ℓ < 346° , |b| < 4° for H ii region candidates with predicted 6 GHz continuum peak brightnesses ≳30 mJy beam-1. We detect radio continuum emission toward 730 targets altogether including previously known nebulae and H ii region candidates. By averaging ∼18 RRL transitions, we detect RRL emission toward 206 previously known H ii regions and 436 H ii region candidates. Including the northern sky surveys, over the last decade the H ii Region Discovery Surveys have more than doubled the number of known Galactic H ii regions. The census of H ii regions in the Wide-field Infrared Survey Explorer (WISE) Catalog of Galactic H ii Regions is now complete for nebulae with 9 GHz continuum flux densities ≳250 mJy. We compare the RRL properties of the newly discovered SHRDS nebulae with those of all previously known H ii regions. The median RRL FWHM line width of the entire WISE Catalog H ii region population is 23.9 km s-1 and is consistent between Galactic quadrants. The observed Galactic longitude-velocity asymmetry in the population of H ii regions probably reflects underlying spiral structure in the Milky Way.