I do a lot of trotting, cantering, and galloping, as well as lateral movements when trail riding, but thats my job. My boss really stresses that its our job to make sure that the horses we train can and will do everything, and be calm about it. We’re lucky enough that our conditions are rarely limiting, and we have access to a lot of great fields. I too get bored just walking, so I spend a lot of time long trotting and loping, except on my own horse who is still pretty green.
As for the question about riding a fast walking/gaited horse with slower horses, my general rule of thumb is to match the faster paced horse. Now if the slower horse is really green, or has a green rider, then the slower horse dictates the pace.