The only concern I might have with using 1x's is keeping it from bowing horizontally over a long span. I realize that the majority of the force will want to bow the beam up, but once things get a little off plane when swinging or getting in or out of the hammock, thin beams can get a mind of their own. Certainly worth a try though. Maybe over something soft.
I haven't tried this yet, but I have seen a few structures that use pre-stressed PVC poles in slight arcs as supports. I'll sketch up a little something and hit the Depot later to see what available supplies exist. I'm picturing maybe 2 PVC arcs that act like a suspension bridge and take some of the load while you are in the hammock. Probably connect to it will a few straps or even a complete material sleeve. Might combine them into a canopy kind of thing for outdoor rain fly.
This has started to go off topic. I will start another thread to continue this part of the discussion. Unless anyone else feels this should continue here.