As everyone knows there were a lot of big Kings in the river this year.  Since I do not use a net, I play the fish to shore and let it beach itself which works pretty good where I fish.  Had this one King half out of water on the shore, put my rod down on the ground and grabed the line near the rod tip and worked my way to the fish.  He then made a 90 degree turn and swam off pulling the line out of my hand.  All I could see was my rod going after him.  The only thing I could do was do a belly flop on my moving rod in about one foot of water.  Well I got my fly rod, but was soak down to my safety belt around my waders.  Sure glad I saved the rod and reel and it was warm out!  The fish broke off!!!

i also beach my fish in shallow water.
i never take my hand off the rod for the very reason you just wrote about.
once they are on their side in inches of water i strip several feet of line out so i can reach down with needlenose or hemo and grab the fly and give it a twist.
i do screw up lots of hooks that way but it gets the fish loose fast and the arthritis isn't so bad i can't tie more flies yet.
oh ya as for the picks i get the camera out while the fish is still in deeper water so i can start clicking as soon as it calms down.

I usually beach them as most times I don't carry a net.Get them on their side then give some slack line and grab line and extract the hook with my pliers.If they decide to continue the fight I either grab the rod if it's close or pull the hook off,whatever is best.