Jittering parallax layers

I had an issue last week with jittering/wobbling sprite objects that made them look separate to the scrolling artwork, especially evident when the camera was slowing down to a stop (smooth camera extension on platformer character, or just a regular follow on X with lerp). I solved this by enabling round pixels in the game’s properties. But the background and foreground parallax layers still wobble and take a moment to stop moving when the camera has stopped. The wobble from left to right for a bit, as if they can’t decide what pixels to occupy. Does anyone know why they continue to wobble when the base layer, and any objects on it, are fine since I enabled round pixels?

A typical event for my parallax layers is below. It works great with round pixels turned off, but that means my base layer objects jitter, so that is not a solution. The only other way I can get my game to behave is to turn round pixels off and have a linear speed camera: no smooth acceleration or deacceleration. That would be a last resort. My game is 1920 x 1080. Thank you.

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