Suggest you try MIT interconnects on the CD player. Also, you may want to investigate the AH! LS Noise Killer filter. This is a series filter you connect to the tweeter connectors on your speakers. It effects a subtle roll off of the highs. I have B&W DM 602s2 which have metal dome tweeters and the AH has sweetened up the sound nicely. It only costs $50, but I don't think it is returnable.
Upper midrange glare prominence --
I am not sure this is a cabling issue. I have an Arcam Alpha 8R integrated which is warm, Paradigm Studio Reference 20 v.2 monitors and a Denon DCM370 (Burr-Brown). I have been spending a lot of time auditioning cables to counter the metal tweeters in the Paradigms--both speaker cable and interconnects. I have become aware of another problem--no matter what cables I listen to--it seems like voice and guitar are whacking me on the head as I listen. Too prominent. What are counter-measures for upper midrange problems like this?