Tailoring tweeter output

Many companys recommend listening with grill on, like Avalon or Dynaudio. On stereophile measurements, the grill changes direct output from the speaker significantly. I am experimenting with this, any recommendation on specific material. Does the reflected from the padding/grill sound create any issues?

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Not sure this is a good idea. What are you trying to accomplish?
Recently listening nearfield and find the ribbon tweeter too hot. trying to decrease out put from 8khz and up.

I used to listen with grills off. Now I prefer the sound with the grills on. With the grills on I hear the music. The speaker becomes more seamless as if the speaker grill is the first stage of room treatment.

Sure, you might hear more detail in some area of the sound without the grills, but it be at a price.
I see you've spent alot of time optimizing your set-up positioning. Covering the tweeter with some material in addition to the grill might work, but there will probably always be a trade-off. You might try less toe-in and move the speakers closer together to compensate. Another option is to try some different cables.
The Ribbon tweeter has very wide dispersion so toe change will not work. The 3-5Khz region will drop before attenuation of the tweeter.

I am adverse to cable tuning to decreased 8-12khz output. Any cable that accomplish this would limits bandwidth.
After looking at pictures of your system I see the problem.
You are set up on the short wall. Your speakers are too close to the side walls.
Can you arrange your room so your system is on the long wall. The sound will be much more pleasing.
The room is a complex part of the system.
I hav tried the long wall setup. It is the same with much more bass issues.

I have also moved the speakers 3' from side wall and this does not change much. The direct sound of the tweeters are measuring a little too hot, this is done by setting gating time low to minimize the side wall reflection.
The problem with acoustic attenuation of your tweeter's output is that any material absorptive enough to make a significant differnce down at the bottom end of your tweeter's range is going to be overly absorptive in the top octave.

Assuming were talking about the Sarastros, I would consider experimenting with maybe one inch thick open-cell foam along either side of the tweeter, cut so that the sides are V-shaped, sort of like the faceplate's angle around the tweeter diaphragm. The idea is to allow the tweeter to output unimpeded across a reasonably wide arc (maybe 90 degrees or so), and then attenuate its output beyond that arc. We want the foam to be thick enough that it will effectively attenuate energy at the lower end of the tweeter's range. I really don't know if this will work or not, and several tries would probably be necessary to fine-tune if the initial try is promising, but I think this has a better chance of making a net improvement than placing absorptive material in front of the tweeter.

RAAL uses 2 foam blocks to adjust radiation pattern these reduce output slightly. Maybe sim will work. But better to just use a attenuator on ribbon if its to hot near-field. Or replace loudspeaker many ribbon loudspeakers do run tweeters hot since at distance they reduce in level. I use designs with user adjustment so can be used near or normal set ups. Fostex r100t is very good for attenuation.
I understand it's an old recording engineer's trick to drape a piece of toilet paper over the tweeter to tame the high frequencies. I've tried this on a few shrill recordings, and it works pretty well. It does, though, tend to reduce not just the highs in the brightness region but also in the region above that, which adds "air" to the sound. You might give it a try. It's almost free and it's easily reversible.

If your speakers are bi-wirable, you could also insert a resistor between the bass and treble inputs.
How far apart are the speakers?
It doesn't make sense that you can move your system from the short wall to the long wall with the same results. The long wall should give you more options for speaker placement and the ability to increase off axis listening angles.
The fact that the bass was a problem on the long wall was most likely midbass which is easily cured with Tube Trap products along with Tube Trap products for the wall behind the listening position.
I know there are other room treatment products on the market, but it is my opinion ASC makes the best room treatment.
I see you have analized your room to death, but there is nothing like trial and error.
Sometimes we have to take two steps back because we went too far. Room treatment and cables alone are extremely powerful.
This is all a delicate balance and sometimes when we think we need less of one thing we actually need more of something else.
Many thanks to everyone. I will update this as I try the suggested solutions in the future.

I have very rudimentary understanding of room acoustics so I have done mostly trial and error. The long wall setup resulted in a 12-15db peak at 40Hz which is insurmountable to most traps. I even plugged all the ports and treated the back and front wall.

Most of the time, less toe in should reduce high freq energy. My problem is that the midrange driver has a narrower dispersion than the ribbon tweeter.

I think the ASC is great in offering diffusion in combination with bass trapping.

Good luck.

And don't forget to try the toilet paper!

Forgive my ignorance buy why are you trying to reduce the tweeter output from a speaker you love? Trying to surpress the tweeter will be like killing the "air" and sonic life of certain instruments.

By chance have you considered - like in Kung Fu?! - to redirect the energy instead? Use a diffuser on the side walls - 1D works best for latteral diffusion, as in QRD or hemi-cylindrical - and begin with the diffuser in line with your listening chair and push it towards the front wall in 2"-3" increments and listen to the same track over and over again. You'll be surprised at how the sound will change.

I've found that the sound is best when (i)the 1st side wall reflecltion point closest to the speaker is a bare reflective wall, and (ii)the other 1st reflection point from the speaker on the other side of the room is diffused. Floyd Toole in his latest book says that the most significant side wall reflection that is a positive affect in creating apparent sound source width and envelopment came from 60degrees, with looking straight ahead being 0degrees and over your left (or right) shoulder as being 90degrees. You can use trigonometry to find that 60degree mark.

You might also want to toe in your speeakers so that your limited dispersion mid driver is aimed just behind your head while any excess tweeter treble sound is diffused so as to keep the energy and 'liveness' of the sound in tact.

Hope this helps . . .