I tried again at a different time of day, and used a variable ND filter. After several attempts adjusting the settings and the filter I was able to get a lot closer to what I wanted on a single shot. Still not perfect, but better. Anything longer than a 1 second shot still washed out pretty bad, and trying to compensate by turning the filter any farther resuled in uneven brightness. I understand that's the characteric of a variable ND filter to do that. I'm slowly getting there.
Yep... You're headed in the right direction now. And this scene has some completely different lighting than your first sample shot. The lighting, in general, is a lot more even here. 
@CraigPearson wrote:I tried again at a different time of day, and used a variable ND filter. After several attempts adjusting the settings and the filter I was able to get a lot closer to what I wanted on a single shot. Still not perfect, but better. Anything longer than a 1 second shot still washed out pretty bad, and trying to compensate by turning the filter any farther resuled in uneven brightness. I understand that's the characteric of a variable ND filter to do that. I'm slowly getting there.
I like this shot. You have captured a very good starting point.
Now it needs to [have just] a little post processing. Check the dynamic range of whites and blacks, level the horizon, and adjust the highlights and shadows. Finally, go ahead and tweak the contrast and colors however if you want. Done.
@CraigPearson wrote:
Ah, I see. The background is washed out, not the water streams. This is an HDR, High Dynamic Range, problem. I would bet that if you moved about, and took the shot without the bright background, then the problem will be minimized, if not eliminated.
If you are not familiar with HDR photography, you may want to explore it. The human eye can see a wider dynamic range of light than a camera sensor. DR is the difference between the brightest and darkest areas of a scene. Your shot is a textbook example of it, with a much brighter background compared to a darker foreground.
Had you exposed the shot for the background, then the foreground just might be nearly completely dark. When you expose for the foreground, then the bright background becomes overexposed and washed out. So, how do you solve this problem, and get correct exposures on the foreground and background in one image?
Basically, you “cheat.” You would need to take multiple exposures and then use software to combined them into one image. This is not as complicated as it might sound, because the software is usually totally automated. All you have to do is capture a good set of images for the software to work with. It usually takes a minimum of 3 photos, but you could use a larger sampling if you wanted.
