How do I know what my system's

Your experience mirrors mine with the cd playback as I have the same player, the Arcam FMJ CD23. My old Audio Alchemy rig did not differentiate cd playback nearly as much. Good CDs sound good with the Arcam and bad ones sound real bad. Also from a/b comparison with my Denon 2910 (which sounds dark in comparison) the Arcam I think is a tad forward and maybe even to the bright side. Is any of this a bad thing or just the way it is? I still very much enjoy listening to music through the Arcam and to my ears HDCDs sound excellent, I just wish there were more around. BTW, I also have transparent speaker cables. The Classe 6 is a fine preamp, but you may want to consider experimenting by adding a tubed pre. This may mellow out your sound a bit by adding some ear pleasing distortion. If you buy a tubed pre (or get one loaned to you) listen for a couple of weeks and then reinsert your Classe. I think you will find yourself noting the differences. Then decide if you like what the tubed pre did for your system. I went to a tubed pre and gained mellowness but also a widened soundstage. Buy one used and if you don't like it sell it here and get at or close to what you paid. There are several good ones out there in your price range.

A gentle way to enhance your listening pleasure is by means of tweaking, small adjustments developed by clever inventors to yield a meaningful improvement.
A wonderful, almost free, way to tame what you describe as a "tad bright" CD playback system is to try Herbie's Audio Lab "Grungebuster2" CD mat. It is only $12.50, yet the benefits can be startling.
At first, the taming of brightness seemed to be a shelving effect over the high treble range, but after listening to hundreds of CD's there is no loss of treble exension or relative level, rather a loss of the CD brightness which my ribbon tweeters can expose in certain CD's. For the moment, the single most cost effective "tweak" in any of my CD or vinyl playback systems.
The Dakiom Feedback Stabilizer can bring overall naturalness, even refinement, to certain CD players, which can be quite surprising.
A further subtle relaxation in CD tension can follow placing one Machina Dynamica Brilliant Pebbles Mini bottle on top of your CD player, just over the center of the spinning CD.
This does not yet address the issue of whether to try one of the multitude of vibration modifying footers, which is a whole other universe of choices to try (for example, Cardas Myrtlewood Golden Cuboids, or Herbie's Tenderfoot option).
When your source is optimized (and, your spare cash exhausted) you may well settle back into contentment, at least for a little while, not an easy thing to accomplish in this hobby.

I agree with Chazzbo - rather than "weak" link look for a variation on your approach to reproducing music. Think sonic change rather that weakness.

I see your all SS rig and think tube pre-amp or as someone has suggested a turntable. Or perhaps a passive preamp. Maybe a CD player that has been noted for its smoothness and edge free reproduction. Look for changes to make your system a bit more forgiving of bad recordings and warm up the midrange.

Double wow for the additional advice.

I knew somebody was going to start talking about tubes. Well, I'm totally ignorant on that subject, just know there's a cult following. By all means, recommend a tube preamp and I'll check my local dealers for a loaner or something. But no doubt it's only a short step from there to a tube power amp, and eventually I'll have tubes coming out of the light sockets.

I forgot to mention that I sorta doubt my CD player is much of a weak link, either. I kinda think the Arcam CD23 kicks ass. Maybe it's bright, but the gain in clarity and immediacy (I heard it directly compared to several other models in the price range) was more than worth it.

I'm still leaning toward playing with a used amp; just looking around Audiogon there seem to be tons of options for 2 grand or under. The brands I tend to notice, for whatever reason (I guess because they get talked about more) are these: Bryston, Krell, Classe, Sim, Levinson, and PS. Well, Levinson is too pricey. But if anybody is bonkers for, say, Krells, or Sims or Classe, feel free to let me know. (I understand more power isn't necessarily good if it's sucky power, but these brands don't really suck, do they?) Some used items I'm eyeing right now are:

Krell KAV 2250
Krell KAV 250a (what would be the difference?)
Krell KSA 150 (originally $5000, now $1600, why?)
Classe CA-200, 201 or 301
Sim Audio Moon W-5
Bryston 4B-ST or SST

Thanks again!

Ok, If you have some extra money....Spend it on treating the room...This is you best investment...