How to tame a bright system?

It's obvious that the recording engineer adjusted the frequency response at 2:39 to emphasize the song's presence (upper mids & treble). If this is the rare song that is too bright; find a better version. If you object to the brightness with many songs; I suggest replacing your electronics to a rich warm sounding tube amp & preamp. There's nothing wrong with your B&Ws, they play what they're fed. There are many to choose from; eg. Conrad Johnson has a warm house sound as do most EL34 based amps. After over 50 years mixing & matching and finally landing on a PX25 with horns, welcome to the merry-go-round (part of the hobby).

As others have said, it’s your speakers.  Switch your speakers to classic spendor/harbeth/stirling and your problem will magically go away. I’ve heard the Chord/spendor combo many times and they are a perfect match.  Maybe they are voiced together.  I think they share the same distributor.  

Try replacing the screws on the tweeters with brass screws. Might help. Seems to work on mine. Cheap fix.

Check the tweeter height versus your ear height. I personally like my ear in between the tweeter and midrange. Also, try toeing out to not have the tweeter directly pointed at your ears. Finally, implement room treatment, especially at first reflection points. You'd be amazed at the difference in a well - treated room with appropriate speaker and sweet spot positioning.

Small Incremental Tweaking to the Toe Alignment of the Speakers and Vertical Alignment can reduce the impact of the Upper Mid's and Highs on the Ears. This is a cheap experiment and might produce a improvement that has been overlooked even if it does not completely overcome the frequency levels impaction on yourself.

A Ring Donut of Soft Foam surrounding the Tweeter can have a very noticeable effect on controlling a Intense Upper Frequency, a few Donuts can be produced with differing Hole Diameters.   

The above two suggestions combined might prove enough and is quite cost effective as a method.

Another overlooked cause for such a intense presentation in the Upper Frequencies that are able to be detractors to certain listeners, is if a little too much gain is present through the device matching.

I have a -5db and -10db attenuator on standby for when such a suspicion is aroused. I at present have a -5db permanently in place, as a Pre Amp was able to produce a little too much gain, I can't detect any detriment to the SQ with the -5db in constant use.

As a Cable Suggestion I would recommend a D.U.C.C Wire in a Cable, these are a available from Mitsubishi (Manufacturer of Wire ) or Acrolink. My experience is that they are exceptional at resolving details and have a perception of a richness when compared to other Cables able to produce the detail. There might be just enough richness on offer from this wire to draw back on the High Frequency impact being detected by the ear, and keep the presentation close to the absolute preferred delivery.     

I use D.U.C.C in my System on certain devices and it is used alongside PC Triple C Wires, all Triple C wires can be startlingly revealing, the combination of wires and -5db, create the balance in presentation that is desired by myself.