Good morning 'Stroke,
Yes I do indeed pull my anchor with a ring and A2 float.
However, I do not tie to the middle cleat. The only place you should ever secure an anchor line is to your bow. Never amidships or the stern.
To pull your anchor, you'll snap the buoy on the anchor rope and slowly start a turn to port so you can see your buoy on the starboard bow from the helm.
Once the buoy is on your starboard, accelerate slightly and start a STARBOARD turn.
Watch as the buoy clears the starboard side of the boat, keep the boat on that wide starboard arc or circle as the buoy slides down the rope. Keep pulling until the chain slides through the ring and captures the anchor.
I use a 500' line with 30' of chain and a 30 lb anchor. You will seldom if ever feel the need to drift out a halibut so just fight him on the anchor. Good luck