One challenge that immediately comes to mind when I look at the photo is flow rate. With cobble that large you are going to need significant flow in order to cover the rocks enough to even see the water. You might be surprised at how much water could flow down that without even being seen.
One thing to consider might be to use a different mix of cobble. If you made a mixture with more small stuff ranging in the 3/8"-2-4" you would require a fraction of the flow that your current mix would require, and you would probably love the natural look and feel it creates.
A basic calculation is 1" of water 1' wide requires 2400GPH. If those cobble are 4-6" and it looks to be a couple of feet wide, you could be looking at a very large pump.