Hi @jakeying,
We haven’t attempted what you’re proposing before, which is to push HDMI data over a USB-C cable to the XMOS chip on the Tone Board. However, I highly doubt it would work. The USB-C cable is the physical interface between the Operating System’s driver and the XMOS on the Tone Board.
Without a driver, the data format would be incorrect, hence incompatible.
What the Tone Board is meant to do, is hardware decoding of audio data, stored within .mp3, .flac, .dsd, .dsf, .dff, and other high-quality audio files, into an analog signal for your ears to hear.
If you’re using the analog output from your HiFi system, then the audio-data-stream is already decoded, and there will be no audio performance gains by stuffing a Tone Board there. The muddling that you hear is because the DAC that your HiFi system is currently using, is not decoding the sound files properly.
In other words, you’ll need to stick the Tone Board somewhere after the computing system of your HiFi system.
Computer (HiFi System) ------ OS Driver ------> Digital Signal ------> Tone Board ------ Analog Signal ------> Speakers ------> Ears
Hope this helps! 
See Also: How HDMI Works