The good analog setups separate the clicks and pops from the music.
I don't understand this statement. If one hears clicks and pops, then one hears clicks and pops as part of the musical reproduction. Are you suggesting that some analog set-ups magically make the clicks and pops sound separate from the music?
In a concert hall, the sounds of coughing and gum popping are separate from the music, too, but they are still annoying.
I have listened to my daughter's(does that date me somewhat?) car stereo. She played Elton John's Greatest Hits. Listening to songs that I am familiar with, it hit all the right notes, had great separation, and maybe added some details that I hadn't noticed before. My friend did the same, in his car, with Neil Young's Greatest Hits(or equivalent). You see, in analogue, that would indicate that those cd's were superior. The problem is playing those records at home(in analog)would kill those cd's. What gives?
This clearly indicates to me you prefer the lower resolution and limited extension of vinyl, since the CD playback in a car stereo is lower resolution than in a high end CD front end. In addition, the music is probably compressed via the car stereo system, with the highs rolled off and the mid-bass boosted.
You have not heard a good digital front end. This is obvious. There is not one person who will satisfactorily answer your question. You will have to hear it for yourself through trial and error, along with some guidance available in dozens of Audiogon threads. Do a search for "Best CD player under $xxxx", and go from there.
Futhermore, and I say this with utmost sincerity, you appear to be a perfect candidate for Dakiom Feedback Stabilizers. These are available for sale in the Audiogon listings. In my experience, they make things sound "more analog" by limiting the HF extension of digital playback. At least that's how they sounded in my system, but I can see how they might make digital sound more like vinyl to some listeners. Personal preference is everything where Dakioms are concerned.
Good luck.