Funny that you mention this, because I went down the same rabbit hole with Handbrake and ffmpeg and I still have the same problem too!
Really? *Exhale! People have ripped on me for not using ffmpeg like it’s gonna fix all the problems but this doesn’t sound promising. I posted this a while ago and still haven’t found a solution. 😦
MR, your problem here might just be that your source is HDR (high dynamic range) rather than SDR (standard dynamic range). Regular, 1080p Blurays are usually SDR, whereas UHD Blurays are usually HDR. The HDR color encoding will look muted and washed out on a non-UHD compatible screen, and it probably won’t play well next to the SDR Bluray anyway. (I don’t claim to be an expert on any of this, so anyone can feel free to correct me.)
The clip I shared was actually from an 8-bit, SDR, 4K source, so hopefully it will match the 1080p colors more closely. I’ve also tried to convert it to MP4 for you, so hopefully I converted it correctly and it will work a little bit better: https://mega.nz/file/LkQXRQ4Q#RoVm_ytNAb8yVukbDvCCor-6mFgJKpysRIyPnC5NxIU
(Sorry about the video glitch in the first few seconds; it’s a byproduct of trimming the video in ffmpeg that I couldn’t get around, but it doesn’t affect the parts of the scene that are actually relevant to the puppet show. And again, for anyone who wants to use it, this will need the new LUTs to look correct next to the rest of the scene; I just converted the 4K source directly.)