Do you have two requirements: DVD and Blu-ray disc playback using MC on the NUC, plus 4K playback using Apps on your phone, the Chromecast Ultra, and all with sound through your Receiver?
If we are talking 4K from Apps like Netflix on the phone, cast to the Chromecast Ultra, you could try connecting the Chromecast Ultra to the TV using one of the HDMI 2.0 ports, then using the TV's HDMI port that supports ARC (Audio Return Channel) to send the audio back to the receiver via HDMI. But I don't know if that would work, because the TV would need to support video+audio input on one HDMI port, and audio output on another different HDMI port. That isn't what ARC was designed for as far as I know. Also, using that method you are losing the audio processing of MC and just playing the source audio on the TV/Receiver. Any DSP would have to be done on the Receiver.
PS: Plugging the Chromecast Ultra into an HDMI 1.4 port on the Receiver and playing 4K 60fps to it was never going to work, because the Receiver can't handle 4K 60fps.