I’d be very surprised if 384Khz is actually outputting 384Khz. You can check by playing a some music and listing the ALSA stream values:
cat /proc/asound/card*/pcm0p/sub0/hw_params
Moode looks impressive, however, its a complete and custom image. So, unless we know every customization/setting made for the Moode image, we cant add it to dietpi-software. Also looks like there is no documentation, or sourcecode for this either: moodeaudio (Tim Curtis) · GitHub