I will, however, acknowledge compatibility. I feel more comfortable and "click-ish" on horses with a certain kind of temperment. I can ride a horse the exact opposite of the preferred, but I don't enjoy it as much!
Also, from the calmness you describe, he sounds like a really, really great horse. A very rare kind of barrel horse. Are you going to look at him again? (I still can't believe you can ride him in a hackamore! I've never, ever heard of a barrel horse who could ride like that.)