I would ask how you fight the fish? If you keep your rod up during the fight then it will take longer to land. The best tactic is to lean the rod in the opposite direction that the fish is going. You can use this tactic and actually keep a large redfish from going into your backing.
I had some customers recently holding their sticks up in the air until I got them to hold them sideways. Eveyone one of them then was able to bring the reds in faster. The picture below shows this tactic in action.
I realize a lot of shell in an area is a valid concern but I have experienced no cut offs while using this method. The key is gaining experience in knowing how much to yank without breaking the leader/tippet. I had one guy practice on a fish to see how much pressure he could put on it. He found that he could put a lot more pressure than he ever thought. Another key is to keep the fly line moving, either in or out. It should never be still. Also constant pressure is ideal. Any "jerking' will snap the leader/tippet.
I use 10 lb, 9 foot long, tapered leaders by Climax, Cabelas, and Orvis (non-flouro) (and add (flouro) tippet when neccessary) for years.
This is something I cover in my Kayak 4 Redfish seminar.