If I make a sprite the size of the screen, oriented to always face the screen, will the pixels render 1-to-1, the way they do for panels? My concern is that there might be distortion due to the camera's arc. Will the rays traveling at an angle have to travel farther than the rays traveling straight toward the sprite?

Use a screen entity. If you set the offsets correctly, then it will be perfectly alligned...

however, I don't know what these offsets are, this is just the method 3DGS uses for PostProcessing shader effects.

By screen entity do you mean view entity? I'm not sure what you mean by offsets.

I had the thought of creating a level entity made of 2 polygons and setting the four vertices to the corners of the screen using vec_for_screen, but I'm not sure whether this would get around the distortion problem either.

yes, I mean view entity

No, you can simply use an image. But then (I think) you need to adjust the xyz offsets so it fits correctly...