Omega-type bianisotropic Huygens’ metasurfaces offer a novel approach for controlling the aperture field distribution of leaky-wave antennas. This paper presents a methodology utilizing a parallel-plate waveguide with a metasurface as its top plate. Previous limitations on constant leakage factor are addressed using a slowly varying amplitude approximation in order to satisfy Maxwell’s wave equation, enabling the design of the radiation pattern. A semi-analytical algorithm is employed to obtain the required multi-layer unit-cell geometries. Here, the inter-layer coupling is taken into account, enabling an efficient synthesis of these antennas. Several designs presenting different pointing angles and aperture field distributions are carried out, showing very good agreement between theory and realistic simulations without further full-wave optimization. Finally, the design process is experimentally validated through several prototypes, whose measurements are shown and discussed. These results, demonstrating straightforward semi-analytical synthesis of versatile aperture profiles, would significantly broaden the applicability of such antennas in next-generation wireless systems.