I believe if your TWh does a true running walk it would be a shame to encourage it to trot. We all know how hard it is to get a gaited horse in the correct gait, why force them into something that's not confirmationally correct for them! They were bred to running walk around plantations all day, I don't think it's hard on them endurance wise. What's hard on the TWH is the big lick!!!
Laura "Not all who wander are lost." (jrr tolkien)