Are there tidally locked bodies where the "far side" is denser?

Question

It makes sense that tidal forces lead to tidal locking. Celestial bodies have varying densities and shapes, so some orientations have a lower gravitational potential, and eventually the tendency will be for the body to settle into the orientation of lowest potential, similar to how dice with imperfections, when buoyant in water, will roll until the denser side faces down.

For the Earth and the Moon, it seems like the story is that the denser side faces earth:

The mass of the Moon is not evenly distributed; mass concentrations, called Mascons, lie beneath many of the lunar basins, and the center of mass of the Moon is displaced several kilometers towards the Earth.

However, unlike the die floating in water, in a system of two orbiting celestial bodies (like the Earth and Moon) each body has two gravitational wells. These two areas of lower gravitational potential cause, for instance, the two high tides on earth. The explanation straightforward: Bodies oribiting around their mutual barycenter experience a centripetal acceleration which is equal to the gravitational force only at the center of mass. There is a net inward force on the near side of each body (where the acceleration is less than the gravitational force), and a net outward force on the outside (where the acceleration is greater than the gravitational force).

Since there are two areas of locally lower gravitational potential, it seems equally likely (or at least quite possible) that the mass concentrations of the Moon would end up on the far side of the Earth. Is this reasoning correct? Are there examples of such systems?

Answer 1

a system of two orbiting celestial bodies (like the earth and moon) has two gravitational wells: One with a greater inward force on the inside (where the rotational acceleration is less than the gravitational force), and one with greater outward force on the outside (where the rotational acceleration is greater than the gravitational force). This is what causes two high tides on earth.

I don't think this is correct.

The tidal forces exerted on Earth by the Sun are caused by the gradient of the Sun's gravitational field. The Sun's gravity is slightly greater closer to the Sun and slightly less on the far side. These tidal forces have nothing to do with rotational accelerations. A non-rotating Earth-like planet falling directly into the Sun would have the same tidal forces at 1 AU that we experience on our rotating, orbiting Earth.

Suppose there was a tidally locked moon that was more dense on the far side. A gravitational asymmetry between two hemispheres of any plane passing through the moon's center and planet's center would result in gravitational torque, gradually spinning the denser side of the moon towards the planet. Perhaps unintuitively, tides exert no torques on tidally locked bodies, since there is no tidal bulge lag. So tidal torques might slow the spin, but not stop it. Eventually the moon's center of gravity would be closer to the planet than the moon's geometric center, like our Moon with respect to Earth.