If you can't get him to circle then there's a serious problem and I suggest going back and working on simple respect and obedience (once you rule out pain) and possibly getting a trainer on him to get him jumping SAFELY before you ride him.
He's quite safe, he just runs through my aids. He's sort of a lesson horse. He's not in pain because he's quite happy when your riding him. Doesn't buck, rear, kick, bite, bolt....he just has zero respect for the bit over jumps. I have gotten him completly round on the flat and then I go and jump him through a course and he's a pain. It's not so much with one jump or through a gymnastics line but when doing a course.
Just because he's not in pain on the flat doesn't mean he isn't in pain over fences. The action of jumping might be hurting him, so he pulls and rushes through it and I'm sorry but if you can't even circle him before a jump then no he is not safe. I've seen horses pull riders to big jumps they're not ready for, just because they were accidentally pointed in that direction. He needs these issues addressed before you stop him pulling to the fences.