OK, if you have the low sensitivity mod, you should be all set. Some other theories...
I have not had any particular issue with distortion with my subcard caps, or do I know anyone else who has, but in the particular tapes I've listened to we were all using AT853 bodies, not 831 bodies. I know it's generally recognized that 853 caps can be used on 831 bodies... they fit, they send signal, therefore "it works". But almost surely the electronics in the bodies are different. Does it become problematic under some circumstances? I don't think anyone knows.
If you battery in the battery box is getting weak, that will cause issues. Check the battery with a voltmeter. 9V batteries will generally read more than 9.0 when new, probably 9.5v. When they get down to 7 or 8 they are getting weak, and be sure to check it while the mics are plugged in.
Another thing is quite simply that the subcards seem to have a lot deeper bass response than cards... they sound FAT, as much as some omnis. I'm just saying... they will capture more low end than cards, and if the bass was distorted in the room, these might pick it up accurately, and cards wouldn't have captured it. Keep in mind I haven't listened to your sample (sorry, I can't get to your sample from here), I'm just saying it seems plausible that this situation could occur.