I wouldn’t rule out LuminT3x on WiFi grounds, it is about on your budget and it can easily go toe to toe with even more expensive all in ones and come out on to, often by considerable margins in most scenarios.
I faced the same dilemma as you, that of getting the streamer connected to the internet.
You can try three ways of getting the internet into your Den via:-
1) WIFI via extenders with an Ethernet socket
2) A Mesh system.
3) TP-Link power-line system
All 3 will facilitate you connecting via WIFI only if that’s what sort of streamer you choose or Using the Ethernet route which is sonically equal or better in most scenarios.
You can then use a short CAT8 fully shielded Ethernet cable to the Lumin or another make of streamer/DAC.
Alternatively, if you audition and choose a Lumin, do what I have done with my Lumin X1.
1). Take the same Ethernet CAT8 cable from the TP- Link Power-line into The TP -Link Optical converter which I powered using a IFI- clean power wall wart.
2). I then used 2 identical SFP (small form factor pluggables) which are easily purchased on Amazon and are inexpensive Optical modules. You don’t need the mega expensive power user ones G-tek, Cisco or similar will be perfectly ample.
3). Plug one end of a length of appropriate terminated optical fiber cable, I used 9ft (10GTek LC to LC OS2 Duplex Optical cable) from Amazon plugged into the tiny converter box Optical out with its SFP module inserted. The other end inserted into the Lumin’s superior Optical Fiber Connection via the other SFP Module featured on the Lumin T3x and is identical to the one on the Lumin X1.
This worked plug and play immediately no fuss, no configuration
This is a solid method that eliminates any possibility of RF, EMI, cross-talk and ground-loops as it is effectively Galvanic isolation to my Lumin. I don’t need to worry about any mains interference that could occur from the TP Link power-line using the mains cable to bring in the internet.
I don’t have a super fast fiber connection mine is 150Mb and when I used my laptop to measure what speed and quality I was getting from the power-line it was consistent and solid at 145Mb
I wasn’t a convert to Optical Fiber until I tried it and now I am convinced its total immunity to all the interference from mains an other cable induced issues is what allows my Lumin X1 to absolutely shine.
You could use a WIFI extender into your den and convert the Ethernet out to Optical but I found the WIFI to be less stable that the TP Link Power-line. Mine established a great connection, even though it wasn’t on the same UK type ring main circuit.
I still plan on finding a way of neatly running all Optical fiber 60 ft from my router but it I would be hard pushed to better this connection I currently enjoy.
I found this method of connection to be a game changer for producing pitch black backgrounds from which the most amazing music quality seem to just pop.
So I would definitely audition the Lumin D3 or T3x, both possess qualities that could change your life, The T3x draws more components from the Flagships X1 and now Ux1.