A simple way to get what you want would be to just add a Sonos Connect. Your setup would go like this:
SonosConnect -> C2600 -> MC275
Use the Coax out from the Sonos Connect to the C2600. This will bypass the onboard DAC in the Connect and use the DAC in the C2600. You also need to set the Connect output to FIXED via the Sonos app.
Now you can just use the Sonos app to stream your Apple Music and any other streaming service available via Sonos. Note Sonos does not support hi res streaming... but you aren’t using that anyway via Apple Music. Enjoy.
SonosConnect -> C2600 -> MC275
Use the Coax out from the Sonos Connect to the C2600. This will bypass the onboard DAC in the Connect and use the DAC in the C2600. You also need to set the Connect output to FIXED via the Sonos app.
Now you can just use the Sonos app to stream your Apple Music and any other streaming service available via Sonos. Note Sonos does not support hi res streaming... but you aren’t using that anyway via Apple Music. Enjoy.