Looking for a true upgrade in sound quality

Well, a different DAC would change the sound, but so would a different ethernet cable, or a different digital cable, or different interconnects and power cables.  Everything makes a difference and will change the sound to varying degrees.  All you can do is try different combinations of things until you find the sound that you're searching for.    

No Ethernet or power cable change will give you the performance boost that a DAC will. Bricasti M3 or M1, Chord DAVE used. Get a good USB or AES from Lumin to DAC and you’re set. 

The differences between modern DACs are small but audible.  I've tried a number of different DACs including the PS Audio Directstream MKII, Berkeley Ref2, Denafrips Pontus, Gustard R26 and several others but the very best sound I've ever gotten has been from the Holo May KTE.  You should be able to buy one used for about $4500.  But it is probably wishful thinking to expect that to give you a BIG improvement in sound quality.  Speakers, room treatments, and potentially cords  and cables might all have a more noticeable impact.

A 30 ft length ethernet cable needs some type of clean-up right before the Lumin. Start with the SmoothLAN network filter from Stack audio and for under $300 you may very well get some of the improvements you are looking for. If not, you can return it for a full refund.

I added an ANSUZ MAINS 8 with active Tesla Coils that actually change the structure of the current going into all your electronic pieces and it's the single biggest improvement in sound I've ever added. Mike@ Hi- Fi Loft  NYC.