I know many barrel racers who race in a hackamore. Why not try one of those? Its bitless like your horse likes and still gives you brakes.
However I don't think the issue is with the horse. It sounds like the issue is your hands combined with your horse needing more schooling.
A properly trained barrel horse can run full out in a pattern then come to a complete stand still by just sitting up and deep in the saddle and walk out of the ring quietly on a loose rein.
BB ~ 2014 Trakehner Bratty Mare ~ 1993 CSHA Em ~ 2007 Standardbred