Abstract We explore the degrees of freedom required to jointly fit projected and redshift-space clustering of galaxies selected in three bins of stellar mass from the Sloan Digital Sky Survey Main Galaxy Sample (SDSS MGS) using a subhalo abundance matching (SHAM) model. We employ emulators for relevant clustering statistics in order to facilitate our analysis, leading to large speed gains with minimal loss of accuracy. We are able to simultaneously fit the projected and redshift-space clustering of the two most massive galaxy samples that we consider with just two free parameters: scatter in stellar mass at fixed SHAM proxy, and the dependence of the SHAM proxy on dark matter halo concentration. We find some evidence for models that include velocity bias, but including orphan galaxies improves our fits to the lower-mass samples significantly. We also model the clustering signals of specific star formation rate (sSFR) selected samples using conditional abundance matching (CAM). We obtain acceptable fits to projected and redshift-space clustering as a function of sSFR and stellar mass using two CAM variants, although the fits are worse than for stellar-mass-selected samples alone. By incorporating nonunity correlations between the CAM proxy and sSFR, we are able to resolve previously identified discrepancies between CAM predictions and SDSS observations of the environmental dependence of quenching for isolated central galaxies.