I have been thinking. If this wheel is oriented vertical with the widest/narrowest part to the sides, horizontally, it will be more mass on one side.
Yesterday I put on an iron chain (green) to see the movement of it when I turn the wheels by hand. The chain must feed the widening gaps, and give away chain when the gaps is narrowing. Illustrated direction by pink arrows. The longest arrows illustrate most movement.
The chain I have is very light, only 2.5mm wide, so I could not be able to see if the wheel turns easier one way or the other. I also tried a magnet, but each link in the chain got magnetized and stuck into eachother, stiffening the chain, and increased friction by a great deal.

The chain is allways moving towards the widest gap, and the total displacement in the gravitational field appears to be zero. Because at one side the chain goes up, and the other side the chain goes down with the same amount. So the sum of mass displacement in the gravitational field is zero.
However, what I got left is a greater mass that is constant on one side.
I have a larger 4mm chain I will test today. Maybe it will be easier to see the difference then - if it is any difference at all.

The attached image is just a copy of the previous one, but put on some arrows and lines. I do not have a pucture of the wheel with the chain on yet. I will post this later.

This experiment bugs me a lot. I know gravity is conservative, so something is accounting for the apparent imbalance.

Vidar