Tin Boats came through again with great advice!
I called our local fire dept. and the chief said, "well that's a crazy coincidence, we just retired some fire hose and it's sitting here." I went down and measured, and don't you suppose it was exactly the length we needed to do both sides of our two six-foot dock sections!
The hose was 8" wide, and my dock rails are 5.5" high, so I needed to rip it. Tried a utility knife on it, and thought, "that ain't happenin." So I fired up the table saw, and had the whole 24 feet ripped in just a few minutes. Hint, if you ever do that, keep the hose moving through or the blade gets hot and smokes.
Next I cut it into six foot sections. And lastly, I "stuffed" the just-right-height hose with the skinnier section that was left over from the ripping. That should give it just enough cushion to provide some bumperishness. My plan is to use galvanized roofing nails to attach it to the dock sections.