+1 on the nature of the beast. Look up the Knotty strech-side hammock.
I have also had success with cutting the outer ends off a little before doing the whips. If you hold up the fabric by the short side, I measured from the top corner in about 6" and then down the outer edge about 2". The cut this little corner out, repeat on other 3 corners. Sewed a channel then ran a cord through it and pulled tight for the gathered end. It gets rid of the floppy sides, but makes it harder to sit in, as the sides are tight and push up under your legs. I have a few that this worked with, but have switched to the stretch side now.
You may want to try laying at a little more of a diagonal, IMO.
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