Comparing attaching the rope at B or C.
The lever arm includes the vertical vector?
Assuming vector Fy(b) and vector Fy(c) are in the same vertical plane, and on the same side of the C.B., I AGREE with you. >...approaches to the actual center of rotation<
As drawn vector Fy(b) and vector Fy(c) are on opposite sides of the C.B. at A.