I have found my answer. I tried the W whip, and it didn't help.
I went with a straight whip, grabbed the GT ultralight, and hung it in the same place using the ENO slapstraps. Everything stretched so much, I almost hit the ground. But when I adjusted and it settled, it was at that magical 30 degree angle -- and that's when I realized that the ENO slapstraps are nylon -- the straps I've made are polyester. They don't stretch nearly as much.
I hung the DIY hammock at a 30 degree angle from the get-go, and it lays just fine. The sides are relatively loose, just like the GT ultralight.