New or Old CD Player?

Is the Linn or the Naim more "analog" sounding?

Yes they’re both very analogue in their lower mid richness, without the bass getting thick/syrupy as tubes tend to do.
Good luck finding a the Naim 555 pairing under $10k though, also the Linn CD12MkIII, as there were not many of these, plenty MkI’s and II’s but it’s the III you want, if you can’t get the Naim pair.

https://www.stereophile.com/cdplayers/207naim/index.html

This was the a review of only the MkI with PCM1702 not the better MkIII with PCM1704’s +PMD200 (same as the Naim).
https://www.stereophile.com/cdplayers/86/index.html

Cheers George

The Vitus RCD is a wonderful sounding cdp. You can pick up a second hand one within your budget, if you can find one on the market.   Vitus CD players are the most analogue sounding digital sources I have heard. 

If you want an excellent analog player buy an OPPO 205 before they are gone and have the MOD RGHT modification done.
This player beats them all while giving you lots of additional features. I have one that was just modified and have never heard anything like it. Tubes with a superb DAC (ES9800) produce the best of both worlds on any CD. And the total price ($3800) is well within your budget.

Indeed, imgoodwithtools, you know precisely what you should do:  ARC Ref. CD8.   Lo and behold, there's a real nice, lightly used one on the block here at A'Gon right now, and you don't need to spend $5K.  Its offered by some member goes by the moniker, Whitecap.  Check it out.  

EAR Yoshino Acute Classic   +1.