Hi,
Sorry for missing this.
There’s no official specification for dithering HDR (BT2020) to SDR (Rec 709).
So most devices offer a few ‘curves’ (effectively what we have now) which allow you to cycle through some presets.
Make sure your display doesn’t have different contrast / brightness settings at different resolutions. My TV does this, which has caused confusion before. The easiest way to test is to disable Adjust Refresh Rate so that the 4K clip is played at 1080p.
Sam