According to the technical data on this web page
https://www.hifi-im-hinterhof.de/moon-n … l-techdata
The input sensitivity is: Eingangsempfindlichkeit     370 mV - 3,0 V RMS
3,0 V RMS are 11,5 dBu with a SNR of 110 dB
So if you deliver 3,0V RMS = 11,5 dBu with the ADI-2 DAC, then you achieve the maximum of 110 dB SNR at the premap section of your integrated amplifier.

Now look at the ADI-2 DAC, it has a higher SNR at these Reference Levels:
Rauschabstand (SNR) @ +7/+13/+19 dBu: 117 dB RMS unbewertet, 120 dBA
So we should simply concentrate on the Amp side not too go too low under the 3,0V but also to preserve a little headroom not to overload the input.

13dBu is too high, it results in 3,46V, therefore the distortion that you hear. And the level becomes even higher if you add Bass or Treble at the ADI-2 DAC.

If you would use Reference Level of +7dBu then you would have the full SNR of the DAC at Volume of 0.
On the Preamp side of your integrated amp you have still enough headroom for using Bass and EQ.

There are two possibilities for settings at the DAC

1) fix setting of reference level to +7dBu, then you have 4,5 dBu headroom for e.g. adding 3 dB Bass and 1dB Treble at the ADI simply to put an example for what you need to reserve such a headroom.

But should you make use of different Bass / Treble or even PEQ settings or dynamic loudness where its not easily clear, whether you add something to the signal or lower it, then I would tend to use the next option ...

2) Auto Ref Level settings. Let the DAC calculate the required reference level and watch the display at what volume level at the DAC the reference level automatically changes between +7 to +13 dBu. But set it to the value where the DAC just comes back to use a reference level of +7 dBu. Remember this volume level !!!
But +7 dBu are only 1,73V, you can make it still louder up to 11,5 dBu which is 2,91V.
12 would be too much, as this is 3,08 which is over the 3V which are possible.
So .. add 4,5 volume to the DAC and now you are at the sweetspot of your amp for maximum SNR.
Remember this volume setting as well, louder than that is not possible.

You need to take now simply an operational decision whats more fun for you. Static or Dynamic settings.

If you intend to use features like dynamic loudness or even PEQ B/T settings on the DAC the best would be to use the dynamic settings with auto reflevel.
After changing the settings you need simply to find the volume setting where the ADI-2 DAC is still at reflevel +7.
You see it in the display .. no magic .. simply look.
Then add lets say 4 or 4,5 dBu to the volume and this is your new maximum.
At the end an easy not too difficult task.

It's not the ADI-2 DAC that's clipping, but you amp's input can't handle the +13dBu.
Go for +7dBu Reference level, 0dB volume.

This way there are some few dB headroom for the amp's input electronics.
Soundwise it's usually better not to drive electronics very close to clipping.

The other way around, Reference Levels are at the XLR outputs: +19 dBu, +13 dBu, +7 dBu, +1 dBu @ 0 dBFS
With Cinch/RCA output levels are simply 6 dB lower (+13 / +7 / +1 / -5)

The display shows you the actual reflevel +19 dBu, +13 dBu, +7 dBu, +1 dBu
Together with the information in the manual, that cinch/XLR is -6 dB lower it should be clear.

Our ears work this way, that louder sounds better.
When A/B comparing two different settings you need to ensure, that
- the final  listening level is the same and
- A/B comparisons can be performed quick within seconds
And best performing it blind or double blind ...

Apparently the above is not true for the ADI-2 DAC FS, per MC's comment in another thread: