How do I know what my system's

Skippack,
My compliments on your selection of gear. There is not an obvious weak link in those components and you have not overlooked any items that are essential to getting the best sound per dollar spent. That being said, if there is any item that may seem suspect, it is the amplifier. I would be careful though, about thinking that "more power" would help. If the first watt isn't any good, how many more of them would you want? There are powerful amplifiers that have nothing musical about them so power alone is a poor guide. However, to make an amplifier musical, it must have enormous amounts of power along with sosphisticated design architecture so that it may control the speakers with more precision. If you have not auditioned any tube based equipment, your are limiting your exposure to what is available. (there is alot of bad tube equipment also) Having been a dealer in the Hi-fi industry for 22 years, I have concluded that for myself, the sound quality derived from good, modern tube equipment is unmatched. But, the point is to compare. What sounds best to you is what matters. There may also be faster cabling available. (However, I do like the sound of the Transparent Audio and actually own a pair of Music Wave Super cables). I think very highly of your CD (with the Ring DAC). Your pre-amp and speakers also seem like great choices. You should be able to sell the amp and cables with ease and then be able to invest in a different type of design that refines the rest of your system. As far as a turntable goes, 2k is probably minimal for a phono stage and turntable system, but that too would be very enjoyable. Just another opinion that I hope helps.

I would demo a Conrad Johnson preamp or at least try a good tube preamp.

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.