Tsunami Squares is a computationally lightweight tsunami and inundation simulator which utilizes a unique cellular automata technique. We make modifications to the underlying algorithm which result in increased accuracy and enhanced waveform resolution. These improvements leave Tsunami Squares well suited for machine learning applications where large pre-computed tsunami simulation databases are required. Previous implementations relied heavily on a smoothing algorithm which acts as a moving average applied to the water surface heights and velocities to eliminate anomalies at every time step. Although this allowed the simulation to function properly, it brings several unwanted effects such as reduced wave detail and lowered energy. A solution is found by shifting the location at which the water surface gradient is calculated, reducing the amount of anomalies in the simulation, and thus lowering the amount of smoothing needed by a factor of $\sim 10$. Also introduced is a new method to conserve energy locally, compared to previous methods which reference a simulation-wide energy calculation. We make comparison tests were made using the 2011 Tohoku tsunami along with the 2010 Maule tsunami to demonstrate the improvements made.