sag with structural ridgeline
Sounds like you've identified your variables accurately: rain protection from tarp, ridgeline length (hence hammock sag). You choose. I printed out a paper protractor for some rough measurements of support rope angles when I was calculating forces on main suspension, ridgeline, and hammock ropes, and was surprised to find that my hammock rope angles were greater than 30 degrees (closer to 40). That's probably because I've adjusted my hammock design to let me lie with my feet a bit lower (and different hammocks require different adjustments). My choice in setting up is usually to make the hammock as comfortable as possible. All three parts of my suspension (main suspension, ridgeline, and hammock ropes) are whoopee-adjustable, so if I'm concerned about wind and rain I can raise the hammock by either shortening the hammock ropes or lengthening the ridgeline. I've also devised a way of lowering the tarp, but that's another story.... Good luck. From your picture, it looks like your ridgeline might be adjustable. That's a good place to start. Lengthening it may require shortening your main ropes to the trees.