How to reduce unwanted ringing on the high undamped strings?

Have you tried a treble cut in EQ3 in the effects section? It's not the same as 'equalizer' - confusing, I know, but the manual explains the difference.

You can simply set the Last damper slider to max in PTQ Standard and then all the notes would get dampers. Of course that is highly unrealistic and deadens the sound - the sympathetic resonances of those ringing undamped higher strings is a big part of the piano sound. Then there's the sympathetic resonance slider which you could also decrease.

Only in Pianoteq Pro could you target specific keys to, say, change impedance/cutoff/Q for those higher keys.

In Standard you could also reduce the volume of the offending notes one by one in Note Edit. As was suggested, you can use the demo version to try any possibility before buying.

I have Pro but, from the manual:  ...This note per note adjustment is available in the Standard version only for tuning and volume.

Also, on the site:

[3] PIANOTEQ PRO lets you edit 30 parameters for each note on your keyboard. In PIANOTEQ Standard, you can explore this feature with the volume and the detune parameter.

You may get some comfort by physically reversing your headphones (from L/R to R/L) if none of the above good advice helps.

Hearing issues are not fun, if you love sound. There are all the above remedies, but of course, nothing is perfect in terms of everyone's infinitely different ears.

Compromises must be made if you need to protect your ears from further damage. It's not often spoken about but pianos can damage hearing, even if subtly. You can over a long number of years get used to louder bass on the left, and treble on the right. So turning your earphones around on your head can sound wrong - at least in the beginning. Persist and you're going to some extent toward training your ears, rather than hammering home a form of natural conditioning. If audio is not important, consider this poppycock and disregard (some like to try to keep ears balanced by not subjecting to long hours of strongly biased signals as much for health, as for work reasons).

If you can live with not using a player preset (bassy left and treble on right), try the "AB" presets which both Steinway D and the Bluethner have. They are good sounds (to me) but have more bass on the right and the higher trebles over on the left. It's maybe the way to play without maybe doing more lossy things to the preset, by changing behaviours/EQ too much etc.

Thanks to everyone for the suggestions.

dazric, I went back and played with Equ3 again. I'm familiar with parametric EQ from using it with electric guitar. Unfortunately, although it does reduce the ringing, it also leaves the lower registers dull.

My own idea for EQ'ing the 880 headphones to get rid of their upward "bump" from around 6kHz to 10kHz didn't work at all with the external Apple EQ plugin - the problem wasn't latency but degraded overall sound. However I found I can just add some extra control points to the Equalizer in PianoTeq to manage this. It helps a little which may be enough for the moment, as none of the pieces I'm currently working on spend much time in the very high registers.

At some point I may play around with the demo of Standard a bit more - thanks to everyone who proposed specific things to try out in Standard.

Lastly, Qexl, thanks for the idea of reversing headphones or else trying out the AB presets. I haven't tried either yet but I will - smart ideas that as you say might do a lot while reducing the quality of the piano model as little as possible.

Success! I found this did the trick for me. The first minute or so it seemed strange but I very quickly got used to it. And my right ear is more comfortable this way. Thanks again to all who replied.

P.S. to dazric - Thanks for the idea about reverb presets. I have been fiddling a bit w/ both Reverb & Delay, and actually I find that Delay typically contributes more to excess brightness (and thus excess "ringing") than Reverb, at least for the presets I tend to use. Typically I end up either deactivating Delay entirely, or else either sliding the wet/dry mix for Delay more towards "dry"; or else using the tone slider to make the delayed sound less bright.

Thanks for the suggestion - my previous tweaks (especially wearing the headphones in reverse) are still working well, but I'm intrigued by your idea & will give it a try, just to see.