The past two nights I have had a significant breakthrough in hammock comfort and excellent sleep. And it is all about the pillow.
First I tried a full sized USDA regulation pillow. Great for laying in the hammock reading, but I would need medical attention if I spent a night with it cranking my head up. So I tried to make do (all this experimenting in my garage hang) with folded up fleece vests or sweaters like I might well do when backpacking. Better than nothing at all, and especially useful for stopping cool breezes that want to run down my neck.
But then I dug out my Mont-Bell inflatable pillow that is part of my ultralight backpacing kit. Inflated it somewhat less than half way (ridiculously loose and floppy till you get your head on it). This is absolutely perfect. And it is better than perfect when I put it in a cotton pillowcase (I find it much much nicer than laying my head on rubberized fabric).
Exped also makes an inflatable pillow - probably even nicer than the Mont-Bell. An overpriced luxury that I cannot recommend too highly. At some point I will probably fool around with some polyester fluff making a DIY mini-pillow and see if that is better yet, but this is so good that there is little motivation for further experimenting in that direction.
The best thing yet. I sleep like a dead man. And although I am a side sleeper on the ground, with the hammock and this pillow setup, I find sleeping on my back entirely to my liking. Maybe this is old news to everyone.