Recently a hybrid-type terahertz (THz) pulse source was proposed for high energy terahertz pulse generation. It is the combination of the conventional tilted-pulse-front setup and a nonlinear crystal with a transmission stair-step echelon of period in the hundred-micrometer range etched into the front face. The tilt angle introduced by the conventional tilted-pulse-front setup (pre-tilt) was chosen to be equal to the tilt-angle needed inside the nonlinear crystal (62° for lithium niobate (LN)) in order to fulfill velocity-matching. In this case, plane-parallel nonlinear optical crystals can be used. The possibility of using a plane-parallel nonlinear optical crystal for producing good-quality, symmetric THz beams was considered the most important advantage of this setup. In the present paper, a thorough numerical investigation of a modified version of that setup is presented. In the new version, the tilted pulse-front is created by a transmission grating without any imaging optics, and a wedged nonlinear optical crystal with a small wedge angle is supposed. According to a 1D numerical code, significantly higher THz generation efficiency can be achieved with a transmission stair-step echelon-faced nonlinear crystal having a 5 - 15-degree wedge angle than with a plane-parallel one or with the conventional tilted-pulse-front setup. Because of the spatially-dependent group-delay dispersion introduced by the transmission grating, a small wedge in the nonlinear crystal improves the spatial homogeneity of the THz-generation process, resulting in higher efficiencies and better beam profiles. At 100 K temperature, and by using 800 nm pump pulses with 20 mJ pulse energy, 100 fs pulse length and 8 mm beam spot radius, approximately 4.5% conversion efficiency and close to 1 mJ terahertz pulse energy can be reached with the newly-proposed setup.