Looking for a true upgrade in sound quality

You may have others who agree here, but your statements are contrary to the knowledge of a massive majority of network engineers, physicists, and other scientists, etc.

@jji666  Classic denial.  And yeah, there are tons of people here who agree with me.  The vast, vast majority of very experienced audiophiles here have achieved significant improvements with upgraded network switches/cables and streamers because everything matters when it comes to streaming and matters a lot, so make no mistake that you are in the extreme minority here when you say they have no sound and it is critical that the newbies also understand that.  

What I said about streamers was that they weren't something to "match" with analog components as tone controls

@jji666 No, in that other thread you literally said word for word that streamers have no sound just like you did about switches and network cables here.  I’ll go find it and copy it here if needed.  If you wanna walk that back somehow, fine, but you absolutely said that streamers have no sound so don’t try to say otherwise. 

Many people who actually understand networking are very skeptical of network tweaks. Switches and network cables don’t have a sound, except silence when not working.

@jji666 Many people who understand networking refuse to just use their ears because they’ve convinced themselves something can’t possibly make a difference. You’ve also said streamers have no sound so let’s consider the source here. It’s fine to be skeptical, but dismissing something without hearing it is arrogant and ignorant — but it’s a lot easier, I’ll give you that.

As others mentioned, particularly in your situation the first thing I’d do is try a filter before your Lumin.  This SmoothLAN filter has been getting pretty rave reviews on another thread here, and at $254 with a trial period I’d consider this an absolute no brainer to try.  
https://stackaudio.co.uk/product/smoothlan-network-filter/

After that and if still looking for further improvements I’d try a Lampizator DAC although there are many other outstanding choices at your budget from Bricasti, Weiss, T+A, Meitner, etc. that would all likely provide a significant and very meaningful upgrade to the DAC in your Lumin.  Hope this helps, and best of luck.