Jason, here is how it works. The vast majority of DACs operate in sychronous mode on all inputs except for USB. This means the source/transport provides the masterclock, and makes sound quality highly sensitive to the quality of this clock.
There are some exceptions to this, in which the DAC buffers and reclocks ALL inputs (asynchronous DACs), most notably the PS audio perfectwave MKII in native X mode.
Since computers provide very crappy clocks, USB converters and most USB DACs are asynchronous, meaning the DAC / converter buffers and reclocks the signal.
What does this mean? Since you're only concerned with computer audio you can do two things:
1 - Get a USB converter that provides a very low jitter clock to your DLink III. You can spend between say $500 for a good (e.g. JKSPDIF Mk III ($460), to $3500 (offramp 5 + Turboclock + power supply) for a SOTA USB converter, or any amount in between (Audiophilleo 2 with Pure Power ($999), Wavelength Audio WaveLink ($900), Offramp 5 base model ($1200))
2 - Alternatively, you can get a very good USB DAC, which really is the asynchronous USB converter and DAC in one box. I listed a few options in my previous post, but these DAC run between say $1,500 for the Wyred4Sound to $4000 for the PS audio Perfectwave and Empirical Audio overdrive. The Ayre is somewhere in between.
Again, in my estimation the USB dac route is more cost effective has fewer boxes, and I suspect will give you better results than keeping the DLink III.
You can easily rotate a few USB converters through your system, since most manufacturers offer 30 day trial. If this solves your problem for $1000 or less, you could keep the Dlink III. If not, move up the food chain with a better USB DAC (some of which probably can also be had on 30 day trial).