Electron-positron pair production in strong electric fields, i.e., the Sauter-Schwinger effect, is studied using the real-time Dirac-Heisenberg-Wigner formalism. Hereby, the electric field is modeled to be a homogeneous, single-pulse field with subcritical peak field strength. Momentum spectra are calculated for four different polarizations - linear, elliptic, near-circular elliptic or circular - as well as a number of linear frequency chirps. With details depending on the chosen polarization the frequency chirps lead to strong interference effects and thus quite substantial changes in the momentum spectra. The resulting produced pairs number densities depend non-linearly on the parameter characterizing the polarization and are very sensitive to variations of the chirp parameter. For some of the investigated frequency chirps this can provide an enhancement of the number density by three to four orders of magnitude.