I would definitely stop him chewing the fuzzy bits off, as that might end up building up in his crop and causing impaction. One possibility is to make the blankets less appealing by making other parts of the room more interesting (you could invest in a play gym or place perches and toys on the outside of his cage), but I suspect your best option is not having him in a room where your blankets are. You could also try distracting him with another toy, though it seems likely that he will keep trying to play blanket forts and getting mad at you when you try stop him. I'm also wondering if he is a she and he/she is being nesty, in which case you will certainly want to keep him/her away from the blankets.
He sounds very happy, and the beak grinding is contentment. My birds do it before nap time.
