Turn HDMI-CEC(BRAVIA SYNC) off in all of your devices. It will make a mess of things. Use just the #1 HDMI output on the UBP-X800 for audio and video into the BD/DVD input of the DN-STR1080 for BDs and DVDs. In the UBP-X800 System Settings, set the HDMI output at Auto. In the Audio Settings, the Digital Audio Output should already be set at Auto. Connect a coaxial digital cable from the UBP-X800 into the DN-STR1080's SA-CD/CD coaxial input. The coaxial input should be set to SA-CD/CD by default. Set the sound mode for the SA-CD/CD input at 2CH Stereo.
With these settings, you can turn on the receiver and set it to the SA-CD/CD input and then turn on the UBP-X800 to play CDs without the TV coming on. With the SA-CD/CD input set to the 2CH STEREO mode, you can just play a CD without having to change the sound mode anymore. Switch to the BD/DVD input on the DN-STR1080 and turn on the TV to watch movie discs using the UBP-X800. You'll change the sound mode here as needed based on the track in play to get the desired sound. Nice setup, enjoy!