Is there a way to change the background color this way?

Red: below the 200-period moving average.

Green: above the 200-period moving average.

You can kind of do this.

You could set the background color to green. Then add a 200 period exponential moving average to the chart with the Plot Style set to Area, the Area Fill Color set to Red, and the Fill Opacity dragged all the way to the right.

But then you would probably want to re-plot everything eles on top of this again (including adding another price history plot), to get the stuff on the bottom to be not be covered up by the fill of the exponential moving average.

Thank you, Bruce ! 

You're welcome.