Six months ago, I spent a week at the shore. It happened to be full moon. We were out walking late at night while the moon was high up, and had to slog through ankle deep water on the way back. It was like clockwork roughly 12 hours apart.

Did read through stackexchange. It is indeed complicated. But the top response feels like paralysis by analysis. If we analyzed turbulent flow too much we would be unable to build rockets. Remember frictionless planes and point masses in high school? Those results are not exact either but a great way to model and understand what is going on.

Soooo .. could we make simplifying assumptions here? What if the earth was a smooth rigid sphere with a layer of water on the surface? The center of mass of Earth-Moon is at ~3/4ths of the earth's radius, from the earth's center. They are rotating about that center. The 12+ hour tides in many parts of the world start to make sense. Is there a mistake in this mental model?

Your clock was off. Tides advance ~30 minutes per day. But not exactly 30 minutes. Sometimes more. Sometimes less. Sometimes it doesn’t follow a semi diurnal pattern.

Water can’t pass through landmasses, and that is a huge factor. If the earth had no landmasses, the tides would be entirely as you expect. However, if you look at a global visualization of tidal heights, you will see that a small landmass, NZ is a great example, can have highs and lows just miles apart. Same in Panama, what happens on the pacific coast is wildly different to what happens on the Caribbean.

In addition, the gravity of the sun comes to factor as well. Where I am, north of the 50th parallel, we simply don’t get very low tides during the day when we are near the winter solstice. The opposite happens in the summer.

The timing of the tides for any given spot tend to be predictable (where it is semi diurnal anyway, other places are a mess). But heights are extremely variable.

The SE answer gave you a nice map. The points where the white lines coalesce experience no change in height. The blue regions experience low tidal amplitude, whereas the red regions experience high tidal amplitudes. The white lines are the lines of equal phase: if a point on the line is experiencing its high tide, so is every other point on the line, and likewise for low tide.

As is clear from the map, the tidal response is profoundly affected by land mass and ocean depth, which have complex shapes; so too the tidal response is as complex as it is, which is simple in comparison.

From reading the accepted StackExchange answer, I think the answer to your last questions is that this model might still be too simplified.

In your simplified model of the Earth, you would also need to make the ocean deep enough that the water could travel fast enough to keep up with the Earth's rotation (~22 km).