My advice is the opposite of @kota1 . The DAC is the most important part of a CD system. If you have a DAC you like, then you are really just using the CD player as a CD transport, sending a digital signal to the DAC.
Streaming you are fighting bit losses as large files are sent over the internet. I don't know for sure, and maybe someone who knows can speak up here, but I think CD players are much closer to "lossless". If that is the case, there is not much to be gained.
The key to digital is to get a DAC you like and it sounds like you have. Once you have that DAC, I would never use the DAC in a cd player.
Jerry