Streaming a CD over the network

[CenTdemeern1]

I bought a bunch of CDs recently, and I only have one device that can actually play them- my Linux laptop. Normally this wouldn't be much of a problem, but now I want to be able to be in a voice call with someone else on my *Mac* while being able to listen to the music on the CD.
I decided I wanted to approach this by streaming the CD's playback over the local network by using VLC's Stream feature, but then when I tried it out it wouldn't start the stream and instead just start local playback.
This happened specifically when I wanted to use my CDs. It works fine when playing local files or when trying to stream JACKAudio output (though that seemed to be peaking weirdly so I kind of don't want to try that again unless someone has a solution to that. I tried lowering the volume, it still sounded weird and distorted).
Does anyone have any suggestions on how I can deal with this and play my CDs over the network?