Jason...
I have the DAC 10.. Not the 10H. It does not have such a provision to turn off outputs to use headphones in this case. I now realize too late I should have bought the DAC 10H, but at that time my neighbors never complained about my audio. I received that dreaded knocking on the wall from my neighbor and was forced to look into the headphone option for my night time listening. Now I am stuck trying to run the DAC10 without preamp (93 volume) and improvising my preamp/ headphone via my old HAP100. So now I am stuck until I find a new place to live without neighbors on the other side of my wall.
But, if I the balanced - unbalanced outputs run simultaneously, I may try a dedicated headphone amp if I find it warrants it. I do prefer speakers over headphones at this point. Found a used pair of Sennheiser HD650's. But, life goes on. It can lead to better things out of finding a new need that one was not looking for.