Longitudinal piezoelectric coefficient of a twinned ferroelectric perovskite material with an array of partially compensated head-to-head and tail-to-tail 90-degree domain walls has been studied by phase-field simulations in the framework of the Ginzburg-Landau-Devonshire model of BaTiO3 ferroelectric. In particular, it is shown that the magnitude of the build-in extrinsic charge at the domain wall and the nanoscale domain size can both promote rotation of the static polarization vector within the body of adjacent domains. This polarization rotation drives the domain closer to an orthorhombic state, and the proximity to this ferroelectric-ferroelectric phase transition is directly responsible for the enhancement of the properties. Our simulations and the theory also suggest that the same system with nominally overcompensated charged walls may show a negative effective longitudinal piezoelectric coefficient. The obtained results can be used for quantitative estimates of piezoelectric properties of domain-engineered crystals.