I need the Apogee, as I do record. I could sell the E10K. I could add in a little extra money as well, if necessary. Is the Schiit stack a good match for the HiFiMans?
Not so much a match, but I'm guessing the Modi/Magni is a little better at bring out the best of any headphone, over the E10K.
Nothing against the E10K, but the Modi DAC chip has a higher SNR and the Magni is a more powerful amplifier.
You might be able to find a used ODAC/O2 with in your current $200 budget.
On Ebay you could get a used Modi DAC or used ODAC DAC.
used O2 (Objective 2) amp or used Magni amp
And stay with in your $200 budget.
Used Modi (optical) DAC, $53
http://www.ebay.com/itm/351627538780?_trksid=p2060353.m1438.l2649&ssPageName=STRK%3AMEBIDX%3AIT
Assuming you have a source (Mac) with an optical output port.
Used O2 amp, $76
http://www.ebay.com/itm/331774475127?_trksid=p2060353.m1438.l2649&ssPageName=STRK%3AMEBIDX%3AIT
So for $129, you might have at least a small improvement in audio quality, maybe even more then a little.
Once you have the Modi/O2, you can sell off the E10K.