Hi Dr Anna and others,
I have something more to share with this and I may have another solution to offer you and others who are experiencing this annoying issue. 😉
Through my testing, I have ascertained that the issue is localised only to the use of AirPods on an iOS device, with soundcheck enabled and even then, it only affects certain tracks. That's only part of the story though and in doing some slightly more advanced testing, I've figured out a little more about how I think Sound Check is (probably) working and what might be going wrong.
For my test, the song I am using is Chris Cornell's bond theme from Casino Royale called "You Know My Name". On my iMac, via iTunes, the track plays perfectly. It also plays perfectly on my iPhone through the onboard speaker. The distortion kicks in only when I connect up my AirPods with Sound Check enabled from either my iPhone or iPad.
The distortion can be described as a crackly horrible sound that happens when an audio source is turned way up beyond the point that it should be listened to and it loses its clarity and becomes unlistenable as it breaks up. Turning down the volume helps to mitigate this issue - hence the way that, at least for me, switching off Sound Check makes the song sound perfect, though you have to become a human volume adjuster from song to song, which is annoying and defeats the magic of Sound Check, which is designed to alter the volume from song to song, to save you having to do it manually.
Ok, so to look a little closer, I grabbed the "You Know My Name" file in my iTunes library and opened it up in an external music waveform editor and pulled open that app's playback controls, which include an audio (dB) monitor and a volume slider. Playing the song at full volume through a pair of inexpensive TDK bluetooth headphones renders horrible distortion akin to what I have been hearing on my AirPods, but usefully, I could see the dB going into the red zone on the audio monitor on the screen (indicating distortion), so I pulled the volume slider down to about 50% and the distortion was still there on the monitor (and my ears) - so I reduced the volume further to about 15% and the distortion went away pretty much completely and the song sounded perfectly good.
Right, so how does this help you out, well, unfortunately, what this means for us all, particularly if we want to enjoy Sound Check (which we should, because it is truly great when it does work) is that we are going to need to mess with the songs in our iTunes library on a case by case basis, when we experience distortion. In practice, the way to do this is to look at the distorting song in iTunes, select it and hit Command-i (Control-i on a PC?) to get the song info window, then click the File section, look at the "Volume" value for reference and see that it says -10.3 dB (which is nowhere near enough of a volume drop for my file) and then head into the Options section of the window and go to the Volume Adjustment control and drag the slider down, in my case I had to pull it all the way down to roughly -75% on the slider, then sync your iPhone/iPad again to send a new version of the song to the iOS device, connect up your AirPods to it and give the song a test run. For me, it now sounds fine with Sound Check enabled. You may also need to experiment with different EQ settings or turn the EQ off altogether for the affected songs.
(My speculative footnote - it appears to me that the "File" section -> Volume value in the song info window is the value that is being used by Sound Check when that song plays, so if it isn't cutting the volume enough, you get horrible distortion when Sound Check is turned on).
Sorry about the long post - it's been a long day, but I hope this helps you out.
Cheers,
Max