The noise is not affected by volume control so line out mode will make no difference. As Rob Watts stated the noise is coming from the display so there is nothing you can do. Perhaps someone can spread a light on why I can hear it through active speakers and others cannot through an additional second headphone preamp using headphones. I'm sure there will be a technical reason for this.
The reason is simple: The external amp acts as an attenuator, while the digital loudness level is set to (near) maximum. Feeding a power amp directly will result in the full level of the noise, while the digital loudness level is attenuated.
In answer to your question about second headphone pre-amp: because it sounds better. The Hugo TT amp section is actually not all that good compared to the competition, particularly for phones such as my LCD3F, though even phones such as my AKG812 which are "easy" to drive sound better through the V281: warmer, smoother and with a bigger sound stage. All very subjective of course.
I don't question your preference, but I'm not sure if you're aware that it's dedicated to coloration and harmonic distortion. As Rob Watts would say: «Some people like harmonic distortion.»
Now this behavior of your amp apparently leads to a better synergy between the TT and your headphones (not to forget your ears and your sonic ideals), and in my experience harmonic distortion makes the sound more forgiving anyway – helps with masking the inevitable tonal flaws in the reproduction chain.
Your statement «The Hugo TT amp section is actually not all that good compared to the competition» is fundamentally wrong, since the «amp» in the TT consists of some short conductor paths or wires. It's the DAC's output stage which drives the headphones, and the same path is used for the line outs. A perfect headphone amp would sound like the TT's headphone output; the deviation between the two variants shows the coloration introduced by your amp. If you're not satisfied with the TT's (line/headphone) output, you should choose a different DAC instead. Any attached amp will have to deal with the signal from said output – there's no bypassing.
But I see your dilemma: The sound is more to your liking via re-amplification, despite the objective signal corruption. But there's a solution: Instead of making the sound more forgiving (e.g. warmer) you could also make it more neutral, less dependent on forgivingness. The solution is called equalizing. Once your headphones are equalized to sound passably flat (with respect to your personal HRTF), you will moreover experience a refreshing increase of resolution and transparency – a result of reduced masking effects. Moreover you're free to shape the sound to your liking without adding distortion (instead of relying on the amp's «factory preset»).
I wish there was more open-mindedness on Head-Fi. Some people strictly refuse to use equalizers, they even consider their approach puristic, at the same time they have no problem with adding needless electronics components to the signal chain with the goal of euphonizing the signal.
