Nope I don't know how you could do it. And I honestly don't think you should. Maybe we aren't being clear here. You have a horse that a lot of people put a lot of years of selective breeding and work into having that exceptional, different gait. That smooth gait is what sets his breed apart from (and some would say above) a quarter horse.
Barrel racing is not done at a trot. Many Walkers can canter/gallop without affecting their gaits, so if that is your only concern, it shouldn't really come into play.
To take all the generations of work, effort, blood sweat and tears, and undo it for selfish reasons of wanting to barrel race a horse entirely unsuited for barrel racing, is kind of a terrible thing to do, in my mind.
Either barrel race him at his gait and accept you have a horse that is never going to be a primo barrel racer (even if he could trot), or find a sport better suited to his style, or sell him to someone who does love what he is, and get yourself a horse that DOES suit your own needs. Your doing a greater disservice and cruelty to the horse in undoing what he has been bred for, then selling him on to someone who will love him for exactly what he is.
I have to agree with the others. Gaited horses have been bred to be gaited for ages, trying to ungait them is basically impossible and really, quite unfair to your horse. If you want a barrel horse, get one bred to do that job and enjoy your gaited horse for what he is.
I used to own TWH's and you can't change their gait to a trot. They are naturally gaited and trying to train them not to would probably only irritate the heck out of a horse because he won't understand what you want.