High-directivity antenna systems that provide 2D beam steering by rotating a pair of phase-gradient metasurfaces in the near field of a fixed-beam antenna, hereafter referred to as Near-Field Meta-Steering systems, are efficient, planar, simple, short, require less power to operate and do not require antenna tilting. However, when steering the beam, such systems generate undesirable dominant grating lobes, which substantially limit their applications. Optimizing a pair of these metasurfaces to minimize the grating lobes using standard methods is nearly impossible due to their large electrical size and thousands of small features leading to high computational costs. This paper addresses this challenge as follows. Firstly, it presents a method to efficiently reduce the strength of "offending" grating lobes by optimizing a supercell using Floquet analysis and multi-objective particle swarm optimization. Secondly, it investigates the effects of the transmission phase gradient of PGMs on radiation-pattern quality. It is shown that the number of dominant unwanted lobes in a 2D beam-steering antenna system and their levels can be reduced substantially by increasing the transmission phase gradient of the two PGMs. This knowledge is then extended to 2D beam-steering systems, where we demonstrate how to substantially reduce all grating lobes to a level below −20 dB for all beam directions, without applying any amplitude tapering to the aperture field. When steering the beam of two Meta-Steering systems with peak directivities of 30.5 dBi and 31.4 dBi, within a conical volume with an apex angle of 96 • , the variation in directivity is 2.4 dB and 3.2 dB, respectively. We also demonstrate that beam-steering systems with steeper gradient PGMs can steer the beam in a wider range of directions, require less mechanical rotation of metasurfaces to obtain a given scan range and their beam steering is faster. The gap between the two metasurfaces in a Near-field Meta-Steering system can be reduced to one-eighth of a wavelength with no significant effect on pattern quality.