This is a bit of research in progress.
Since discovering that the MoonTides can shift, I have been studying the shift. I have found that the shift need not be an integer number or hours. On a given day, other cycles can shift the tides a bit. I am studying the mechanisms for that. This chart shows the MoonTides for July 30, 1998 shifted just 19 minutes to the right. With that tweek, MoonTides got the major turns, within 4 minutes, in an UP-DOWN-UP day.
So where did the 19 minutes come from? I don't yet know. Stay tuned.