A:Answer I figured it out! Make your own button. The problem might be solved a number of different ways (and using different apps), but here's the route that I took:
I downloaded and purchased the Button Remapper application from Google Play (something like $3 or $5). I believe there's an option for it to automatically start when the TV is powered on. If so, you'll want to checkmark that box. Then, I used the Add Button menu to add in the Red, Green, Yellow, and Blue buttons. (I've never seen those buttons used for anything.) From there, I set the Blue button to perform the Action named "System Settings". From that point on, whenever I'm watching video (an HDMI input or an app such as Amazon Video or Netflix), when I press the Blue button, the Android settings pop-in on the right-hand side of the screen and I can navigate that to adjust picture settings.
Be aware that most/all of the picture settings only apply when you've got a video playing. You might be able to adjust backlight, but not all the others. An easy test would be to adjust the Hue one way or another (and then set it back to 0 when you're done). If you're inside a menu or something with still pictures, you may not be able to adjust its appearance.
Oh, and once that's all done, you might want to remap the Red, Green, and Yellow buttons to something you're likely to use on a regular basis. Perhaps as a shortcut to some of the other streaming video apps, like Disney, Hulu, CBS, Amazon, etc? Enjoy!