It's not exactly what you asked, but I'm a little high: if you could decouple the propulsion systems you could go faster. Just like you can't dangle a magnet in front of a boat to get it to move while it is attached to the same boat

But it reminds me of this:

An article-

https://www.wired.com/2013/07/why-are-these-caterpillars-climbing-over-each-other-the-surprising-science-behind-the-swarm/

And a video(s)-

https://youtu.be/kbFMkXTMucA

https://youtu.be/JMi20j0rkVg

Edit:

Also, looking at the picture again and rereading what you wrote: I feel like it'd be like the difference between a person walking parallel to a person walking on a conveyor belt that's running the same direction they are. Something would be moving you along as you are also moving.

I back that up with the fact the elephant will only have one foot off the ground while walking same as a human would, and their spiderbowl feet would keep it moving forward at a constant rate same as the conveyor would

It's just relativity of motion depending on the frame of reference. For instance, if I have motorised shoes and am walking on an elephant running on a train that progresses on a large ball rolling on a treadmill (with friction) while a monkey is running on the ball in the other direction (without friction); relative to my dog sitting on the couch (with friction), the couch is immobile.