Maximum tidal heights vary widely across the globe, from 16 m in the Bay of Fundy to mere centimeters elsewhere. These variations are due to coastline and shoreline differences. This makes it difficult to determine a global average ocean tidal maximum height. Let's assume the Earth is a landless planet covered throughout by an average one km of ocean. How can we calculate the maximum ocean tidal height from a new moon or full moon syzygy, assuming semi-major Moon & Sun distances?
I think you would have to get into the fluid dynamics. A uniform ocean approximation would help a lot. With any luck rather than solving for a fully 3D time dependent flow, an assumption that the result is an expansion of a few well choosen spherical harmonics, with the same periodicity as the tidal frequency might yield a closed form solution (if you are lucky).