I went out to REI and bought some tubular climbing webbing like this:
I made a loops on the tree end and passed the length through (a DIY slap strap) and made a loop close to my hammock. It seems to hold up great! Spent some time in there and so far, no stretching. I haven't been able to spend the night on it yet, but I think it this will do the trick.
Thanks for the suggestions,