@nathanueasy...

I can "side sleep" in my hammock, and it's a 'gathered-end' hammock! (no "diagonal" nonsense!), but there's a slight catch...

First, I tend to hang a little high (about chest height, so I have to hop up and roll into my hammock. The height leaves plenty of room for my pack. But I also string my hammock somewhat close to the ridgeline. The advantage is I can side-sleep with ease, but I can ALSO stomach sleep if I want to!!

The [slight] trade-off is the closer you string to your ridgeline, the more unstable the hammock is... IF... you're sitting up. Otherwise, it's awesome!

Sorry, can't help with the "wiggling".