Your original need for music with good fidelity for desktop use seems to be forgotten in this escalating more... bigger... more... bigger... spiral. So, let's take a step back.
First of all, the Schiit DAC is a huge waste of your budget. In the OP, you were keen on a USB connection, perhaps, due to readily available USB ports and a desire to not open the PC. Just add a cheap sounds card to your PC (it is easier than you suspect) and run optical or coax cable. This one is $20 shipped on Amazon,
http://www.amazon.com/gp/aw/d/B0045JHJSS/
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A NAD integrated with optical or coax and Paradigm Millennia One 2.0 seem to be on your mind and will do just fine. The speakers roll of at 100Hz so a subwoofer is mandatory. Even the higher end NAD integrated you linked does not have pre-outs. But, KEW gave you a way to make this work. But, the kludge writing did not appeal to you and rightfully so. It was not the ideal way to connect things up, especially if proper bass management is desired.
The Yamaha S301 I initially recommended accepts optical/coax, has bass/treble/loudness controls and a subwoofer out. Accessories4Less also has a couple Onkyo Integrated amps that will do it. They've been mentioned in this thread.
That said, none of the integrated amps in your budget do proper bass management. An entry level AV receiver from 5 years ago will do a better job. It is not just about doubling the signal. A crossover is needed to make the mains and subwoofer blend. Additionally, the timing needs to be controlled. Slapping a Phase knob on a sub amp is not the way to go about this. The Denon X4000 linked before, in 2.0 mode is more powerful than any of the integrated amps mentioned here and fits your budget. I would urge you not to write off AVRs.
I'm not a big fan of using speaker levels to route signal to a powered sub. If you want a subwoofer in the mix, commit to a processor that does bass management correctly.
A complete departure from this will be the minimalist approach, Audioengine D2 and A5 or A2+ with a subwoofer.