I ended up buying the one linked in this post below. It claims to support HDR and Dolby, and has the ability to downscale the second output to SDR, preserving vivid colours from the lights. This is a bonus, since the led lights get washed out in HDR/Dolby. It should allow the proper signal to get through to the tv while sending a downscaled signal to the lytmi box.
It arrives tomorrow. I'll post the outcome.
https://www.amazon.com/Splitter-l-b-y-Vision-Atmos-Scaler/dp/B07VP37KMB