How can we have missed this opportunity?

That dac  doesnot bring anything special a cable conversion your biggest gains 

are from the start , a good lps power supply from your router to start ,the wall wart is junk and just adds more noise, then a respectable ethernet hub at minimum 

LHY. SW6, or better and quality ethernet cables , your best one at your end point ,

that’s even before you get to the dac and its design and filtering and D to A  conversion and use quality power cords , EVERYTHING COUNTS  !,

Actually a REALLY GOOD DAC, with a superb clock, well buffered, fed by asynchronous USB, will isolate the signal, and hence SQ, from upstream issues in the digital domain.

Put your money in the DAC first.  95% of the cost of my digital domain equipment is in the DAC and an "atomic" clock.

In the analog domain I do agree with you.  In the digital domain bits are bits BUT timing and noise rejection are critical, and that is what the best designed DACs add to the system.

As an experiment, while streaming, unplug the RJ45 cable from the streamer.  The music will probably continue, unchanged for some time.  

Why not put up some photos of your system in Details.