A couple of other notes here.
You can use the API-650 approach and calculate all those variables to 12 decimal places, but you're still dealing with a highly approximate design.
So in actuality, there's not a lot of difference between that 0.5 and 0.42 factor.
Note, for example, that the entire approach calculates the "ideal" elastic response, then divides it by 4 or 3.5 or 2 as the case may be because the actual response is nonlinear and inelastic and more highly damped, etc.
So some of those factors come out of committee votes, and people trying to decide if you want X percent probability of exceeding in Y years, or W percent probability in Z years or what.
The theoretical sloshing wave is a single uniform wave in one direction. But there are some swimming pool videos that illustrate the actual seismic waves, and they tend to be more chaotic and more 3-dimensional than you visualize. In this video, note especially the round pool at about 1:10.
I think you'd be hard put to even define what the sloshing wave height was in that pool.