LC technology is a promising hardware solution for realizing extremely large RISs due to its advantages in cost-effectiveness, scalability, energy efficiency, and continuous phase shift tunability. However, the slow response time of the LC cells, especially in comparison to the silicon-based alternatives like radio frequency switches and PIN diodes, limits the performance. This limitation becomes particularly relevant in TDMA applications where RIS must sequentially serve users in different locations, as the phase-shifting response time of LC cells can constrain system performance. This paper addresses the slow phase-shifting limitation of LC by developing a physics-based model for the time response of an LC unit cell and proposing a novel phase-shift design framework to reduce the transition time. Specifically, exploiting the fact that LC-RIS at milimeter wave bands have a large electric aperture, we optimize the LC phase shifts based on user locations, eliminating the need for full channel state information and minimizing reconfiguration overhead. Moreover, instead of focusing on a single point, the RIS phase shifters are designed to optimize coverage over an area. This enhances communication reliability for mobile users and mitigates performance degradation due to user location estimation errors. The proposed design minimizes the transition time between configurations, a critical requirement for TDMA schemes. Our analysis reveals that the impact of RIS reconfiguration time on system throughput becomes particularly significant when TDMA intervals are comparable to the reconfiguration time. In such scenarios, optimizing the phase-shift design helps mitigate performance degradation while ensuring specific QoS requirements. Moreover, the proposed algorithm has been tested through experimental evaluations, which demonstrate that it also performs effectively in practice.