As I understand the DCX, it has input/output level controls, as well as one for the sub output. These levels should be high enough that the sensitivity controls on the amps can be lowered, thus decreasing the noise floor. You'll need to make sure the input of the amps isn't over-driven and you'll be able to listen for noise level, to make sure it's not excessive. I would use balanced line level connections once you have sent the signal to the processor- there's no good reason to convert back to unbalanced.
You want to do as little boosting of levels as possible because along with the signal, comes the noise. Set it to unity gain and work with the output levels and power amp input sensitivity controls to get the most from the equipment.
One way to find the maximum clean level for the integrated amp is to decrease the input level using the control on each amp, play a CD (test tones or music) and turn the volume up until you hear distortion. It won't be loud because you have turned the power amp inputs down and the distortion will be more audible than at high SPL (where the ear/brain compresses and ignores some things). You'll be able to use the meters on the DCX display for this, too. If it's in the red, make the proper adjustments. Once this is done, go to the ouptut control section of the manual and find out how to use the meters to maintain unity gain in the DCX. Once this is done, decrease the level on the integrated amp's volume control and increase the power amp input controls to about half. You may find that this is all you need but for maximum power output, increase them until you notice a bit of background hiss with no input signal.
Look for a Zero Bit .wav file online. This will be useful for listening for the noise level without blowing your ears out and registering on the USGS seismograph.
As always, RTFM.
