Craig and I met after the West Coast swing in 2003, and he told me he was literally four-putting—and he was worried it might be mental. I watched him putt and had great news for him: His stroke was terrible. His putterhead moved on an arc, but it was on an arc opposite to the one I teach. His putterhead moved outside the target line on the backswing, then back outside on the follow-through.
Even though he needed to make a dramatic change, he was relieved because he understood his problem and knew he could make the mechanical adjustment. Now, his clubhead swings on a slight arc inside to inside, and it's the only lesson he's ever taken. I don't know how many millions in prize money he has won since then, but it looks like it's working OK.
Recently, Craig added the claw grip, and I have no problem with that. It helps his right arm work around him, which makes it easier for him to swing the putter on the proper arc. I don't care how a player holds on to it. I just think it's going to work best if you swing on plane.
My stance is narrow and my forerams and my elbows look very relaxed at my sides. People often pull their shoulders up toward their ears and tense up when they putt, which doesn't let them swing the putter on its natural arc. I'll tap them on the shoulders and tell them to let the air out. I often see their shoulders drop a couple of inches after that. Understanding and feeling the tension release will help you free up your stroke.