Displaced walk cycle loop

Hey there,
What would be the best way to preview a displaced walk cycle? Most people make walk cycles stationary. I usually do that too! but for this particular project it’s more useful to animate it displaced because it’s extremely important to have specific displacement in pixels. But I’m having trouble animating because it doesn’t loop smoothly, obviously.
Ideally the preview window could be moved via script, can that be done? then I could just run the animation and the preview window would move 8 (or whatever) pixels at the end of each loop. A hacky solution but it would mean the world to me right now.
Another, less convenient solution, would be to replicate the current tagged section displaced. Only one copy means at least I can see how the transition from the last to the first frame is going. I would have to run this every time I make a change to the animation but it’s a solution.