Basically you want a gain stage on a fixed line level. There's no DAC in the world that allows that, at least none that I'm aware of. You should stop complaining about the X3 line out for a moment and try to focus on your amp, your issue seems to lie there (I'm not trying to be rude, I swear).
I don't have your IEMs, however I'm able to use the EarPods and the Philips O'Neill The Specked with the X3+E12 combo (the E12 have much more power compared to the C&C BH).
Did you try to switch between the OUT1 and the OUT2 sockets on the C&C BH? Some users reported some differences.
Did you set the amp on LOW gain? Did you set the LF switch to OFF (it adds more bass when ON, if I'm not mistaken)?