Not sure if this is to any help, but I have had some HDMI audio trouble with the NUC6CAYH as well.
Tried several Linux distros, and the only one that had audio working out of the box was Linux Mint, this was on a 34" Dell monitor.
Decided to try installing Kodi on the NUC, connected it to my Panasonic TV and installed Libreelec 8.02, no audio with the default setting, had to change audio setting in Setting > System settings > Audio to the following.
Another thing, I tried to change the Video Settings in the BIOS on the NUC, and found that if I change IGD Minimum Memory to 512 MB and IGD Aperture Size to 512 MB the Audio on Video playback was missing, but GUI sounds was ok. Changed IGD Minimum Memory to 64 MB and IGD Aperture Size to 256 (Default) and the audio was back.
So if you have changed the Video Setting in the BIOS, try change it to the above.
I am on the latest BIOS (38) and HDMI Firmware 1.66
So I bought the same NUC and followed your directions. However, I'm having stuttering issues with 10 bit 4K video. I am stunned. All four cores are maxed out almost as if its not using the hardware to decode. Is there a setting or something I should check? VAAPI is enabled.
edit: I found the modded build and it works great.
Could you please share which modded build it is and a link.