There is nothing wrong with the technique you are currently using, in fact its probably the most logical approach to the problem. I use a very similar methodology, especially when I have to shoot through a fence or barrier at a baseball park or the local zoo.
Being a Nikon user, I can not offer specific instruction on Canon's menus (and lacking the model of your camera I am not sure which APS-C to look up), but look for the option to instruct the camera which AF point to use (probably labeled Single Point AF or along those lines). By forcing the camera to AF against one spot, you wont have the repeated refocus attempts before the desired area is in focus.
If your camera has a cross-type focusing system for one or more AF points, you will find that those point(s) will provide the best performance for this technique, even if that means using the center point and panning more after getting the shot in focus.
While this article does not directly addresses your question, it offers useful information to you, and in fact recommends doing exactly what you have been, Lock Focus, Recompose, Shoot.
If Manual Focus is at all an option for your work, you can focus on an object at a known distance similar to where your subjects WILL BE and then track your subjects until they enter focus before shooting. This requires time to track and quick timing when the subject hits the space focused on, so it may not be a solution for your situation.
Finally, an advanced method... Use a lens with a wider depth of field, as little zoom as you can stand, as high an ISO as shooting conditions allow, a faster shutter, and a slightly lower f-stop can help to create a larger in-focus zone, this will help with the timing too, as the precise moment to open the shutter is longer. A tool like this might also be of help in planning your shots. This technique is finicky and can produce aberrations. It also produces pictures that often have to be post-processed before they are an optimized result.
If none of these methods work well for you, it might be time to consider upgrading to a model with more responsive AF features.