I had a very similar experience with something that sounded like it was walking in the wood with me, then stopped when I did and vice versa. It usually happens when there is high winds, I've determined that when I'm walking I'm keeping up with the leaves that are blowing correspondingly with the wind, when I stop as a gust of wind blows, it doesn't have this added affect with my footsteps as I crunch the leaves and sounds like a bunch of leaves are blowing by, I feel like it's this natural optical illusion, it's pretty neat but hard to explain, the way you explain in detail about your experience sends chills down my spine though.