[vhfpmr]

I can see that the distortion of the earth's shape moves the vertical in the same direction as centrifugal force moves the pendulum, but it wasn't obvious that they necessarily cancel out to zero. It would depend on the degree to which the earth behaves like a liquid and not like an elastic solid, but I suppose the earth's solid crust is too thin to have any significant effect.

[Bored chemist]

It would depend on the degree to which the earth behaves like a liquid and not like an elastic solid

In fact, it behaves like a liquid- it even has tides and viscosity.

If the net effect wasn't zero then, over the aeons, the sand grains and the sea would shift until it did.

It seems Mr Newton was cleverer than me. :-)
When I first considered this problem I thought about it in terms of the forces acting on a grain of sand on the surface of the Earth. That's a nasty calculus problem, and I gave up on it without even starting.

He noticed that the question was equivalent to having a water filled pipe from the pole to the equator which is a rather easier problem to address.
I'm unlikely to get a knighthood, run the royal Mint and be remembered centuries after my death. :-)