What is the best way to tame a slightly bright speaker?

Concur with MotokoKusanagi.  Simple attenuation of the mid and high is the absolute most straightforward fix.  No snake oil voodoo tweaks. 

Get speakers with non-metallic cones.

I would strongly advise against any kind of messing around with crossover values. Any speaker worth its salt (certainly something as high-end as the TAD) has a network precisely tuned for attenuation, corner frequency and phase alignment in the context of the speaker’s impedance. Changing any of those values - caps, resistors, inductors, sometimes even minute changes in resistance from different hookup wire gauge - will throw off that tuning and have unintended side effects. You can’t just "pad" a driver in a typical crossover-based system without shifting other parameters.

The room treatment and positioning suggestions are good, and based on measurements from the Stereophile review you might be able to use the directionality of the coax driver to your advantage. But I think speakers have an intrinsic tonality that your ear will always pick up on regardless of the particulars of the setup. I can hear this from speakers at shows - even if the room is totally dead or bright or unknown, you can still kind of tell what kind of energy the speaker is putting out. In the case of the TADs, in my run-ins with them I noticed a bit of hardness/ringing to the upper midrange/lower treble that I found fatiguing. I wonder if this is what you might be picking up on rather than an actually elevated treble response, especially given that the measurements from the aforementioned review seem quite flat in the upper frequencies, and if anything slightly tilted down in the top octave. If that’s the case, ameliorating with a different amp and/or cables may be more effective. I hesitate to go down the cable rabbit hole in a forum like this, but I’d avoid anything silver or tinned. Audience is a safe bet for natural, un-fatiguing highs, and I’ve also been impressed with Crystal Cable in a few different setups.

Perhaps I missed it in all of the chatter.  What are you running for a preamp, DAC, turntable, etc.  Seems like a lot of very complicated solutions for a simple task.

This may be redundant but get a multi band (31?) equalizer. First line of defense for room treatment especially if your room is small. The judicious application of equalizing bright speakers will more than compensate for the addition of yet another electronic component in your chain.

Also makes a great notch filter for bass traps in a small room as well. I use one and find it indispensable. Not the "purist's" choice but it works and it is inexpensive. Have fun.