Definitely use the HDMI-ARC feature to connect your TV to the 976. It is true that professional installers from the 1990s would use the toslink or digital audio but the audio processing codecs are way beyond that now and HDMI will handle all of the signals. That way if any of the programs or apps on your TV are able to output discrete audio you would be all set. At least part of the techno advantage you are paying for is the HDMI-ARC feature so you might as well use it. As far as the Chromecast it connects to your system as a two channel source through a 3.5 mm jack. You would need an RCA splitter to connect to one of the 976 analog inputs.
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Music system
Model 990/7500/Magnepan 1.6 QRs/Technics SL1200 MK2/Aperion S-12 Subwoofer/OWA3/Sony NS75H DVD
APC H15 Power Conditioner

TV System
Large Advent Loudspeakers/ Polk center/Monoprice surrounds/Panasonic Viera 42 inch/Onkyo HT-RC260/Sony BDP S590/Directv


Home Theater System
Onkyo PR-SC886/Outlaw 7125 Klipsch RF-82 L/R,RC-62 center, RB-35 SR/SL, BENQ HT1075, Outlaw LFM1-EX/OPPO BDP-83/Directv
Harmony ONE
Blue Jeans and Monoprice interconnects
APC H15 Power Conditioner