Tonemapper dithering

I am trying to achieve early 3D games look. Right now I am stuck on restricting the colors of a rendered frame to a specific palette. [HR][/HR]What I had in mind is to use a custom node to find the closest color from a given palette and to display it. I did it and it works great with static images like textures, but there is a problem when I use it in post process material that is set to apply after the tonemapper - the image noisy and unstable.
So I decided to use a simpler code from this topic: The same problem occurs; it looks stable but washed out before the tonemapper, but colorful and shimmery after it. It seems like the default Unreal Engine’s tonemapper dithers an image. [HR][/HR]Post process material is applied before the tonemapper:

Post process material is applied after the tonemapper:

As seen on the image, there is a visible color banding before, and this is what I want. Furthermore, all the visual noise before the tonemapper (like in the top right corner of the image) is stable. But the effects like vignette or bloom are applied after my post process material, so they are still in full color.
The tonemapper tries to hide the color banding, it results in noisy visible dithering pattern (for example, here it is produced by vignette and it can also be seen on the black and white gradient of the box) that changes each frame. [HR][/HR]Is there any way to turn off the tonemapper’s dithering?
My post process material is exactly the same as in the linked topic.
Thanks in advance.