I haven't done extensive listening with it at different voltages, that's why I said I think.
My DAC is a DAC 301 (which is a bit problematic IMO), and I got tired of tweaking it. I have tried 14V and I currently run it at 24V. I have an external regulated supply based on the Twisted Pear board, it's similar to dual TREADs or STEPs.
The sound seems a bit crisper, and more cleanly defined at 24V, but it's subtle, nothing earth shaking. I have about 10 headphones I used, ranging from 32 ohm (AKG K81DJ, Beyer DT660) to 250 ohm (Beyer DT990) and a few others in between like the AKG 271s. The sound is heavily influenced by the opamp used for I/V, which is where I spent most of my time tweaking.
I compared it to itself at the different voltages, but again only briefly. Compared to my X-Fi to CK2III or Mini3, it doesn't quite hold up because of background noise (not totally black). Since it's an integrated device, it's hard to pull out just the TPA6120A2 contributions. However, I've not used it in a 3 channel configuration and the CK2III is a 2-channel discrete configuration.
DC offset of 30mV is nothing to concern yourself with. Your HD650 won't even flinch at that. My situation was different, I had to balance the voltages coming out of the I/V stage by better matching resistors (going from 1% to 0.1%) of the differential outputs of the DAC. The TPA6120A2 was used for gain (2) and differential to single ended conversion to drive headphones. I believe mine is at 14mV now, due to the tolerance of the opamps and the TPA6120A2.
When you're measuring DC offset, try shorting the inputs to input ground. You may be picking up some stray stuff on an unconnected input.
See if you can account for the DC offset by looking at the measuring resistance of your resistors * gain.