No advice on the bit. My mare right now is going in a twisted snaffle, she responds very well to this and I've started her on the pattern. Wonder bits are often very good as others have said.
For getting him to go around tighter and faster, you've got to work at it at the slower speeds. Any problems that you have at a trot or walk is just going to get worst at the canter as I'm sure you know. Do you know how to do spirals? Spirals work really well for applying the same aids that you'll need to get them to turn tighter. It really just comes down to your leg and rein aids though. Make sure that you're lifting up with your inside rein, pushing in with your inside leg until you almost get around the barrel. You then want to push him over using your outside leg up by his shoulder and outside rein, this will help him turn sharper assuming that he works off of leg pressure.
You also want to make sure that he's using his hind end well, this will help him go around sharper and faster as well. One exercise that is really good for barrel horses and getting them to work off their hind end is rollbacks. What you want to do is go to the wall at about a 45 degree angle (diaganoly). Lets say you're tracking to the right, you head diagonly to the wall and once you get near, you sit down in your seat, pull your left rein to your hip and add your outside or right leg to push him off to the left...you're turning him to the left at the wall. I usually say something like, "Hey" (this is what my mentor taught me to say) to let them know what I want them to do.
I hope all of that made sense, I can get a video of the rollbacks if you need one, it's kind of confusing to explain in words.
Annie (myself) - Dixie (my spunky mare) - Snooky (my rock of a dog) - Allister (my very outgoing bunny) - Duncan Idaho (my long lived gerbil).