Could be less messy:
With the HDA-912 set to 2CH, connect it directly to the Chromecast by HDMI. Optical out of the HDA-912 to a small 3-way optical splitter, to the Bluesound and the two Avantrees. Optical splitter ~$15 at Ali, brands: Prozor, Linkfor.
Then sell the HDA-939 to me ;)