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This paper reports on experimentally verified methods to enhance the quality factor (Q) for SiC-based lateral overmoded bulk acoustic-wave resonators (LOBAR) by acting on their geometry. A prototype LOBAR device  was previously demonstrated and showed great potentials for enabling very high Q resonators for applications such as low phase noise oscillators and narrowband channellizers by taking advantage of the intrinsic low damping of SiC. However, the demonstrated performances were far from ultimate and the SiC LOBAR design space has not been fully explored. Therefore, an analytical model has been developed to further understand the LOBAR operation and provide guidelines for Q optimization in this work. The designed experiments focus on LOBAR optimization by exploring the effect of structural dimension variations such as the piezoelectric film thickness (250 and 500 nm) used for transducing the SiC into vibration, coverage ratio (ratio of AlN area to SiC ranging 0.5-2.5%), and aspect ratio (SiC length to width ratio ranging 6-10) of the resonant cavity on the device Q. Consequently, more than 20% increase in Q (from 4250 to 5378) has been achieved at 1.5 GHz, and over 100% increase in Q (from 1900 to 4296) at 2.3 GHz. Additional experimental data also further confirms validity of the analytical model used to describe the device behavior.