There are two basic ways to do this.
If you want to do it the right way, with the best audio and video quality, use MC as the video playback device. Hook the NUC to the TV or receiver via HDMI directly. You can allow audio to be routed through there, or you can send audio separately from the NUC to your DAC via a second audio interface, either optical or USB. No Shield involved, no DLNA needed.
If you're not interested in that, and instead want to pull some kind of stunt with DLNA and the Shield, then buy an HDMI Audio Extractor. It will take the HDMI out from your Shield, pass the video over HDMI to the TV, and extract and send the audio via TOSLINK to your DAC.
The weak link in your audio processing is the Shield and perhaps the TV. MC will do better on the video as well with MadVR. I don't understand the point of making your system depend on DLNA. Everything will be better if you just use the NUC and MC directly for playback.