Last night, I got a bit creative. I've been tossing this idea around for a few weeks, and I finally decided to give it a go.
Basically, instead of using a rectangular piece of fabric to start, I actually used a parallelogram. My cutting angle was approximately 30 degrees. The resulting parallelogram had corners of 60 degrees and 120 degrees.
The resulting hammock has an incredibly flat lay. The lay angle is more extreme than in a traditional hammock. I found that it was much less constricting on my shoulders (not that a traditional hammock is bad). I also found that the "flaps" on the edges were less irritating.
I'm not certain the load is as evenly distributed as in a traditional hammock, so I will have to test it for some time to see if there is a failure.
I attached a few pictures. Has anyone ever done anything like this?