What's the best option for front-view walk cycles, as though the character is walking toward camera?

I have a character wearing a ghost costume (sheet with eye holes), and I've triggered the puppet to do an arm/body cycle so that every time the character lifts one or both of their arms, the ghost sheet is lifted, revealing the character's shoes and part of their legs.

I would like to make him walk, not left or right, but forward, as though toward a camera tracking backward. Visually, I imagine that the shoes might peek under the ghost sheet as he takes steps, and be fully visible if one of the arm cycles is triggered (lifting the sheet). Now, I'm sure that I could make additional layer cycles that could accomplish this... I think.

Is there any easier way or combination of ways to accomplish this look of forward walking, as each leg moves toward away from the camera? What are my options?

Thanks.