It is helpful to know the best way to do it, so it is worth discussing. In general I agree with what you say, especially about throwing everything that floats. If the lifesling was near the COB I would not reel it in, but I am assuming the COB has very limited swimming ability. If the line is close I would not reel it in, but if it is far from him, I would want to try to get it to him, either leaving it in the water and sailing near him, or pulling it in and rethrowing. My preference would be to try to make the circle around the victim so the line comes to him and then use the line to bring him back to the boat. I think that is how the lifesling is intended to be used. Take a look at
By the way, I also keep a polypropylene bagged throwing line fixed to a stanchion, so it is also ready to throw. I hope none of us have to use these tools except in practice.