Hello Andrew -
Listening to Spotify as I write. Can’t help you with an ethernet path (I don’t think). For a long time I’d been running Spotify into my main system DAC via USB cable out from a MacBook Air; from the DAC into my preamp or integrated amp.
More recently I was able to get the MacBook and long USB cable out of the path. I got an Aries Mini (~$500). It does Airplay. I have an Airport Express wireless router in the house connected via ethernet to my Comcast/Xfinity modem. The Aries DS Lightning software residing on my iPhone sees the Airport Express and the Mini. I fire up Spotify on the phone, choose "other devices" (or something like that) from the bottom of the phone’s screen and then pick the Aries. Spotify streams off the internet via cable to the wireless router to my phone and then to the Aries Mini - at least that’s how I think it works. Regardless, it sounds great and I am no IT genius. Good luck. Don’t get discouraged. I think streaming is the way to go. By the way, you have some nice gear in that system.