What is your streamer?
Since you found the CD to sound better than the stream using your DAC that points to the streamer. I think also it seems your DAC is not much if at all better than the one in your CD player.
Ok, no insult intended here. But let’s review the pieces:
CDPlayer = spinner, streamer, and DAC
Streaming system = network, streamer, DAC
I find that streaming is roughly equally dependent on the streamer and DAC. If you have a good quality streamer then the network is taken out of the picture (as it will isolate the system from noise and cache the file in some way before streaming). So, the resultant sound requires both roughly equal in investment. Sounds like you need both.