How to tame a bright system?

Crickets.

Even if auditioning isn’t possible I would try a pair of Harbeth C7es3 xd. I can’t imagine you wouldn’t be happy. They are not overly warm whatsoever like some might have you think. They have a pretty similar frequency balance but with much much smoother upper missa and treble. The tone will a absolutely blow away your 606s. Really they are just in another league compared to the B&Ws and the Kefs. I understand liking your speakers despite their brightness. I went through this with Totema for over 5 years before moving on to smoother pastures. I tried Dynaudio Special 40s as well and really didn’t get the hype. To me they were very soulless although impressive in some hifi ways. ATC and Proac would be other good places to look. I think you will be blown away if you try any of these. I find nearly all speakers from companies who pump out “full lines” lacking. They make a 5in and a 6in bookshelf, then a 5in and 6in floor stander, as well as centers. Then they do it all over again for there mid tier and upper tier. Only to replace all of them every three years. I find it very difficult to believe much or any tuning be ear is done. The companies I’ve mentioned focus on a handful of speakers and make small changes over time but each has been fine tuned to a very high level. Anyways just my two cents but I’d strongly recommend branching out even if it means you have to buy to try.  

"Bright" is definitely subjective. However, I have noticed in my own listening sessions that there is a lot of "bright" gear out there in the audio component world. I think that in their efforts to expand detail and soundstage, many audio manufacturers are now making products that sound brighter than their older models. This isn't a new problem, and it has affected the recording industry as well. I'm no expert, but I would say that this trend started with the advent of digital music. I notice it particularly with digital remasters of older recordings. I personally prefer the older analog recordings on vinyl to just about any other source. 

That being said, I do agree with some of the others who have indicated that B&W make some bright speakers. They'll dazzle you with detail, but their top-end glare can drive you nuts after a while. The one B&W speaker I have enjoyed in all of it's different iterations is the 805. I feel that this is now - and always has been - the most balanced and enjoyable speaker they've ever made. Just an opinion. 

In my main system I have a tube preamp running a pair of class A monobloc amps. I am using a pair of monitor speakers from England. When I finally got this system set up, I found that I could truly enjoy all of my music. Nothing seemed too "bright" anymore. Granted, you can't fix a crappy recording, even with the best audio gear. But most of what I listen to is vinyl and streaming, and it all sounds terrific.

Building a system takes time and money. This can be a very expensive hobby. As many of the others in this forum have suggested, I recommend auditioning different speakers. I agree with the "soft dome" tweeter recommendation (Dynaudio is great), and I think the ring radiators (Aerial, Sonus faber) are really good, too. Also, I strongly recommend giving GoldenEar a listen. I have a pair of these hooked up to a tube integrated amp in a separate system, and they are amazing! 

Anyway, have fun and be patient. It took me five years and a lot of buying/selling gear before I got it right...for me. 😎

Aniwolf +1

While cost isn’t everything, it is something. An ok $599streamer into a $2.5k interconnect and $12.6k DAC means that you are hearing everything (good and bad) that the streamer is producing.

Put another way, at $599 they can only spend so much on parts as they also need to provide for design, marketing, manufacturing & labor so something has to give. I haven’t heard that streamer, but it seems like you’ve found its weakness by paring it with such a revealing DAC.

Upgrade everything ASAP!!