balanced systems usually have more odd order distortion and noise than single ended, as there is 2 amps, the noise is reduced through the common mode noise rejection; common mode meaning error that is of the same phase in 2 balanced lines, which when added in a summing circuit (proper balanced->SE conversion, or simply at the headphone driver) cancels out.
if the error is inverted with the signal it does not cancel, only that which is added during and after that conversion is reduced, so you get more noise from double the parts, but then only minimal benefit on that side, if you have 300->600ohm headphones you still get the extra swing, but if your headphones need more current not voltage it may or may not help as the load impedance seen by the amp is halved.
so when people say you should have balanced all the way, they are actually quite accurate for most usage. its a totally different thing i'm afraid mate, there is no balanced conversion in the dac. The dac (if its a balanced dac) converts a digital file directly into a balanced analogue output, no conversion other than digital->analogue and if its balanced all the way to the headphones, all common mode error and distortion is to a large extent deleted; including error in the dac itself
in the case of the DX100, hopefully it uses both phases of the dac output, so this cancellation will have happened there, so with your setup only the amp stages after that, right up to the se-bal conversion will remain. many of these dac-amps dont use both phases of the dac output they just connect one to ground and use the other one
at the extreme of this you have people connecting amps like the PB2 to an ipod directly, IMO theres not much balanced about that, you get extra voltage swing and cancel the noise that effects the headphone cable....