SLOW MOTION SCIENCE!  Ferrofluid dropping on magnet

I always think of the superpositioning of earth and moon gravity field distorting the normal vector. Along the earth-moon axis, the gravity pulling down just becomes lower at the moon side and higher at the opposite side, but the tide happening at these two places has not to do with that effect, but with the effect, the distortion has around the earth at the sides. The normal vector there does not go straight to earth core anymore, it's slightly rotated or rather tilted and thus water flows to build the tide "mountains" and it flows towards the still normal vector, but that much more depends on the changed orientation of the gravitation normals than their magnitude. If you look at the differential field you get when subtracting moon from earth gravity, you can see the difference vectors go horizontally to earth surface at four angles around the earth. These are contributing to the cycle of four tides you normally have per day, at these four places water flows away and later arrives in the places where the differential field has no reorientating effect. There is an obvious lag time water needs to flow.

The sum of gravity fields mainly influences the geometry of the field and changes where "down" is and then this change lets water flow. The effect of gravity along earth is very small. The earth is so far from the moon that it doesn't go through such a high gradient and difference as the magnetic field strength, so that can't explain earth oceans acting like a giant drop of water, but you are right about the much stronger gravity gradient near a black hole.