If I may, just because a cd player is a few years old does not mean it does not sound as good as a new player. Your unit may sound better, worse or more likely just different than others especially new choices at your disposal. But this is a crux of many in hifi thinking a newer product must be better. Well no, digital audio in the Redbook form has been around for almost 30 years now. DACS are not really just getting better, they are more likely being made more cost efficiently for the most part and in reality the algorithms of the Redbook CD format are well known today. How a CD player is designed and built from the ground up is more of a determinant than as to if it's a 7 year old machine with 7 year old DAC's or even a 27 year old machine DACS.
Now if shopping around for either a new DAC or CD player gets you to liking the sound of one or more well that is great but likely not because your current unit now sounds bad or otherwise obsolete. Odds are your current machine sounds just fine. Buy another 7 year old machine and it may sound different to you with either you liking it or not but only because it is different. Buying a new cd player or an add on DAC may give similar results. I'm not trying to talk you out of buying a new player or DAC, only pointing out that any one you buy is likely going to be more because it sounds different and not likely better to you than your current machine which you are now use to after all these years.
IMO DACS are not really getting better, but change due mostly to home theatre needs in decoding and as a result made to do more. Audio side uses these DACS to tune or retune CD playback but in reality maybe a 20 year old machine well made and tuned may also blow you away.
I am currently playing around with a 2nd generation Philips CD player, it has TDA-1541 DACS in dual DAC setup and is 16 bits with 4 times over sampling. I bought it for $10, after cleaning it up, doing some screw tightening and adding some damping as well as spiked feet it sounds pretty good. It even has a coax digital out so if I want to add another DAC I can. It has the well respected Philips CDM-2 transport which tracks my artificial disc tracking test up to 2.5mm wide and the dual defect tracks of 2 - 2mm wide defects in a row. No other CD payer I have ever owned was that good and this is a 1986 used player.
Anyways I'd if in your shoes likely look at a new DAC because knowing Classe as an audio buff I bet your machine is pretty well built.