Okay, leads, check.
I can understand how he may know the pattern by heart- we are not working on the pattern by walking it. You are working on his paticular problems, which happens to be his turns. In order to get him to turn correctly, you must approach this so that he can understand and retain the information you are giving him. It's kind of like playing an instrument- say you know a piece of music but then you try to play it really fast. It's hard because you can't get everything right really fast. And you try to fix it at high speeds, but it gets really confusing. Same for your horse.
Some horses just don't make great barrel horses. But if you are intent on working with him, then you need to slow down. Walk him around the pattern and observe the difference in his turns. See what he does different. With his feet, with his overall body, his head. Have somebody watch him and let them tell you what they see different at a walk than at a fast canter. After that, you have your goal- to get him to achieve those maneuvers at fast speeds. Start at a trot, slow lope, faster lope, and then finally slow speeds. But don't rush it! Work slowly so that you don't confuse him.