Hello Thorsten,
This afternoon we started to get AK errors again, so I decided to do the slow mode test this evening. I "blocked" our business application and restarted the DB in slow mode.
I then "unblocked" our business application and updated a row from the table ACCOUNTTRANSACTION (this is the table from which we almost always get "AK Cachedirectory full" errors). The DB immediately crashed and I generated the diagpkg file diagpkg-20140106.tgz which I uploaded to the file shared you provided. I hope you can find some useful information there.
Note that when I unblocked the application, it can be that some processes immediately accessed the DB because there are some background threads that I cannot easily control. However the crash exactly happened when I then updated the row (via the business application) so I think that the cause is pretty clear.
Thanks again for your help, let's hope you can find that nasty problem. ;-)
Best regards,
Christophe