Now maybe I'm just sensitive to this issue, but if you have to tighten the cinch three times, you're cinching too tight. Even with a horse that bloats you should only have to cinch up twice. You have to recognize that two or three wraps of the latigo around those rigging rings has a multiplying effect. Even a small woman or boy can make a horse extremely uncomfortable by over-tightening the cinch.
Being as you are a barrel racer, and need a pretty snug cinch while racing, I suspect this is your issue.
Three other issues that can contribute to over-cinching, are too much saddle pad (those soft, cushy, pillow-like pads), too wide a cinch, and padded cinches. For normal riding (western tack, non-performance competition), if your saddle fits properly, you need very little padding, and the cinch need be no more than snug. I recommend a wool felt pad of 1/2-1", and a straight mohair string cinch (not the roper style).
The bad news is that once a horse is cinchy from over-cinching, it's pretty tough to get them over it. You just sort of have to deal with it. It becomes a habitual behavior with them that is hard to get rid of.