"There is a problem, as you said, that when going from a good CD Player to a better one, it does have a tendency to bring to light the difference in recordings."
Recordings are what they are. Don't blame the CD player or system for them sounding different. That is the way it should be. If they all sound similar and not all that great to boot then you may have a problem worth addressing.
A good setup/player should bring to light the differences in recordings. Lesser recordings for the most parts should only sound that way because now the better recordings sound better or at least different.
Train yourself to accept what is in the recording rather than trying to make them something they are not. I find that 90%+ of CDs have something good to offer in regards to sound quality. Few do it all right in the same recording, but if you can cover all the bases by listening to a variety of recordings, then you are in very good shape!
As an extreme example, on my music server, a small % of the 10000+ tracks are cuts I digitally recorded off of old 78s playing on an old Admiral ceramic cartridge rim drive table I picked up for $10 at a yardsale for just this purpose. These tracks have some of the most captivating and lively unobstructed midrange there is. That is their strength. There is also a ton of background noise and not much else to brag about, including an unusual overall timbre, but they are what they are (90 year old early recordings that are easily identifiable as such), and are quite enjoyable to listen to as a result.