Hi Rick, in our early cruising years I tried an assortment of tools and techniques, but have settled on one that works for us. I use a Garelick brand telescoping boat hook to grab the ring and lift it up to hand the line through. I stopped running the line from one cleat, through the ring to another cleat, after a blow cut through the line due to the boat sailing. I now always run the line from a bow cleat, through the ring and back to the same cleat; this to minimize sawing abrasion. I will also run a second mooring line as a back up, again to the same cleat.
All work is done at the bow in calm or light wind conditions. I apply a different procedure in strong winds due to our boat's high free board. In that case I have a long mooring line secured to a bow cleat with the working end run back to a mid ship cleat. I approach the mooring ball from the lee side as if I'm going to land at a dock. Once I touch the mooring ball mid ship I grab the ring, run the line through by hand and secure the working end to the mid ship cleat. Wind will push the boat to line up with the mooring ball and at that time I will move the working end to the bow cleat and secure.
It is almost impossible in a blow to point the bow next to the mooring ball, run forward to grab the ring and hand the line through and secure. Every time the wind will push the bow away before I can thread the ring. And no way can I hold a 35,000 pound boat with a boat hook on the ring in a blow. Believe me I've tried it.
I've been doing it this way for years and it works for me as a solo sailor. I'll let crew help in reasonable conditions, but regardless will apply the sample principles in a blow.