After receiving some help, I was shown a simple work-around to accomplish the scaling I wanted.
Add a child Control node, or any node that can be scaled, to a ParallaxLayer you would like to have scaled children, and add the Sprites (or other visual elements) to that Control node:
- <>: Camera2D
- : ParallaxBackground
- - : ParallaxLayer
- - - O: Control
- - - - O: Sprite1
- - - - O: Sprite2
The Control node, when scaled, will change the scaling of its children as normal.