One thing you might look into is a 1080p passthrough EDID emulator for your display — something like this. I haven't used this particular one but someone else endorsed it for the Steam Deck.
EDID emulators will override the supported mode information your display sends to the source device — in this case, it will "hide" the TV's 4k capability, and tell the Odin that only 1080p is supported.
(Note that these are directional — if you plug them in backwards they won't work. You'd plug this into a dock, and plug a standard HDMI cable into it. If you want to use it with just a USB-C-to-HDMI cable, you probably would need a pair of gender changers.)
For those that reside in the US, here is the link for the VCOM USB C HUB and the EVanlak 3rd Generation HDMI EDID emulator