We did it! Saved the rug that was infested by moths, that is. The moths are gone and the rug is in place, and it looks good. At least for the time being. Since the moths had eaten the fringe off of the ends, the rug tends to unravel like a broken sweater from where the fringes used to be. We'll keep the rug until it totally unravels, though..
Here is the rug on our deck while "demothing" is taking place.