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You can get USB controlled CEC injectors for HDMI.

For a 4K120Hz TV I'd be worried about this adding signal integrity issues - "all versions of HDMI®, including HDMI® 2.0a" doesn't inspire confidence.

My understanding is that CEC can be received on any alive interface, not just the active.

Yes but you will lose 120 FPS/VRR. So for high end TVs not really ideal.