From my experience regular cd player isn’t good as a transport to standalone dac,my suspicion is that the inner dac of the cdp and the analog inner cycle interfering the transmission of the pure digital data out and if so preventing your dac to fulfill is full potential .The best way to go is a dedicated cd transport such as the CA CXC and if you are willing to spend more the Cyrus CDt is excellent option too.
I bought the CXC to my Mcintosh amplification and the improvement was huge:more details,huge soundstage, powerful dynamics and better transparency.You should use a good coax cable too.