Controlling the cosmic variance in summary statistics estimated from simulations is an important challenge for making accurate predictions of their expectation values. On large scales, perturbation-theory-based approaches, such as recent 1-loop EFT, are expected to work well. Thus, one promising direction is to construct a reasonable hybrid model combining simulations and PT. Taking advantage of the fact that the propagator -- the response of the final field to the initial field -- can be measured with little cosmic variance, we propose a possible "stitching" method that connects "tree-level" PT predictions with fully-nonlinear simulation results. This approach is applicable to biased tracers in redshift space, and the PT component incorporates important physical effects such as BAO damping and (potentially nonlinear) RSD.