Hi! Since you requested a review, I looked over your changes here. No problems I can see! I think footpath is great here, but in the future one thing to keep in mind is that you can also add access tags to show who can travel without actually reclassifying the way, if that makes sense. So in the hypothetical scenario where there really was a roadway, but only foot traffic was allowed, you could put 
motor_vehicle=no
foot=yes (or foot=designated).

Again though, from what I can tell, in this case footpath works great here. Let me know if you have any questions, and thanks for your contributions!