Sleep on your side.
Really! If you haven't tried it, do so. I'm a 100% side sleeper in a bed. I can't possibly lay on my back in a bed for more than 30 seconds! But I can sleep very comfortably on my back in a hammock. So, perhaps the reverse will be true for you! I prefer to put my face toward the edge of the hammock with the back of my head toward the center. I find the sweet spot by adjusting my diagonal lay and it's good night, Irene!
Just thought I'd put it out there... . Good luck! (that's me sleeping in my hammock)