You may want to hook up the Cambridge's digital output just to compare stereo with digital input to analog with bypass - analog input and plain stereo mode is a pretty convoluted signal path. I've heard good things about the Cambridge, so I suspect your original assumption (better DAC in the Cambridge than the 970) may well prove true, but the most accurate A/B comparison will be to let the 970 get a digital input.

The 7.1 Direct input can be accessed separately from the DVD input - it just happens to share the left and right analog channels with the DVD input. You can select "DVD" from the remote and still have that using the DVD player's digital connection and then select "7.1 D" from the remote and get the CD player.