First of all, I would too worry about having two pre-amp in a system. Take a look at the N7 functional diagram:
The Line out will go through the Line Drivers in Yellow after the output stage of the DAC (i.e., the LPF)
The Pre out will go through the Line Drivers, Volume control, and Gain control stage.
When we said we should avoid double amping, we were referring to having two volume control and two power amplification circuits in a sound system. By power amplification, we are referring to a circuit that will amplify the signal at both voltage and current levels. The Gain stage in the N7 pre-amp is voltage only, it won't increase the current and is significantly lower voltage gain than the phone amp.
So as long as the JRC volume control in N7 offers good transparency, having two pre-amp in your system will only cause very minimum interference.
What is your N7 volume setting when you connect N7 pre-out to your DAC? I agree with FootLighter's assessment, apparently, you are having an input level mismatch between N7 line out and your DAC line input. A bit abnormal because I only encounter similar cases with some Japanese amplifiers previously because some of those amplifiers are designed to work with 1V single-ended and 2V balanced line input levels.