I have looked at hammock geometry from time to time looking at various things. Usually I am looking at the forces involved, the sag angle, how a structural ridgeline plays into it, etc. Anyway, I often generate sketches and as you know, sometimes they quickly show what is going on. Here are a couple that might add some insight in what you are looking at. Note that I chose to normalize the height the bottom of the hammock rests above the ground.