Tying knots actually worked pretty well.
The knots fulled into impermeability in the wash, so I had to cut them off to hang the wrap to dry. Next time, I'll try to tie them so that they are all about the same distance away from the closest pick.
I'm going to wait until I'm ready to give the wrap away to press it, remove the waste yarn, and trim all of the ends. Part of me keeps thinking I might get a fringe-twister at some point, so waiting to do the final finishing steps makes sense.
Overall, I'm really happy with it.
I also wove the BFL I spun into a scarf and fulled it in the same way. It's quite pretty. My edges look better, to me, at least.