We present a method to flexibly and self-consistently connect individual galaxies’ star formation rates to their host halos’ potential well depths, assembly histories, and redshifts. After parameter exploration, the method is able to reproduce galaxies’ observed stellar mass functions, star formation rates (specific and cosmic), quenched fractions, UV luminosity functions, autocorrelation functions (including for quenched and star-forming subsamples), and quenching dependence on environment over the full redshift range (up to 0 < z < 10) for each observable. Key results include revised stellar mass-halo mass relations, the dependence of average star formation histories on galaxy SSFRs and environment, quenching timescales for satellites, and predictions for the James Webb Space Telescope as well as higher-redshift galaxy correlation functions and weak lensing signals.