After a bit of RTFM for the ADI-2 DAC (section 19.3 in particular), I see no reason to disable Auto Ref. It's basically just juggling digital level control and analog output stage gain for optimum SNR depending on volume level setting chosen. You have a crudely-stepped analog volume (/ gain) control, and then digital attenuation fills in the gaps. I would do the same.
The KH120 is making things a little more difficult than necessary for the amateur without a defined SPL reference level. First of all, the block diagram does not seem to accurately reflect the actual circuitry, as nominal input impedance changes depending on output level setting. (WTF? Plus, I would understand it if the input were at 10 kOhm and padded down via an additional 10k in series to achieve a 6 dB attenuation, but the table says 20 kOhm at 114 dB SPL and 10 kOhm at 108 dB SPL, exactly opposite from what I would expect.) So that setting must be doing more than controlling gain after the actual input stage. Documentation FAIL.
Anyway, the highest output level setting gives 114 dB SPL for a 0 dBu input if the input gain trim pot is all the way up. This is, in all likelihood, way excessive gain, considering that the input can accept up to +24 dBu and the ADI-2 DAC can output +19 dBu, and the speakers will only do 111 dB @ 1 m maximum with a bit of a following wind. (Not to mention you may not even want levels even close in a literal nearfield application. I would be more than happy with about 100 dB SPL.) Chances are that this setting will make some input stage noise audible at close range - I would expect an input noise level of somewhere around -100 dBu. But if you ever wanted to max out the speakers using a little Clip+ or 3.3V-only onboard sound (whose max levels are ~800 mV rms and thus in the 0 dBu = 775 mV vicinity), this would be the setting to use.
Here, I would probably try output level = 94 dB and input gain trim = 0 dB. That'll give 100 dB SPL @ 1 m each @ +6 dBu in. That's easily a low enough level for neither the input stage nor the ADI-2 DAC to break much of a sweat even at this rather high volume, and it should keep noise levels inaudible. +19 dBu would translate to 113 dB SPL, so if you really wanted to blast your ears, you could still do that. If you're running rather low digital levels like I do (ReplayGain + some EQ), 100 dB may be worth a shot instead. One of these two in any case.
EDIT: Not sure why the short delay digital filter appears to be the default for the ADI-2 DAC. As delay in the milliseconds is of no concern to us, I would think the regular Sharp filter would be the better choice. There was a firmware update concerning filters recently as well (check whether that's installed), I suspect there may have been some sort of screwup in selecting the right one. I hope they're making use of the traditional, low period ripple sharp filter that is also included in the AKM DAC chip now.