There's no "agree to disagree" in physics. This is verifiable. I am not totally confident about the vector sum vs arithmetic addition thing at the cable. Make a physical model and prove me wrong. The physical model would be pretty easy.

I am certain, however, about the sin beta thing. A force applied parallel to a lever arm does not do any leveraging. If you do not take this into account your program produces incorrect results.

For a gut check, consider a set of cantilevers with horizontal arms (I have some). As you make the yoke shorter, the cable pull is more and more parallel to the arms, and MA decreases. If the yoke cable could become horizontal, MA would be zero and you would not even squeeze the arms together.

And if the forces in the lower cables do indeed add as vectors, you would want a yoke as long as possible and more nearly parallel to the vertical cable, so that those forces don't cancel, right? But your model says the opposite.