Can an AES-256 key be generated for a large number of cribs?
Just the most basic research on this site would have told you, the answer is NO.

From all known cryptanalysis on AES, the answer is simply there are no useful plain-text attacks. (Which is essentially what your "cribs" are.

It's not going to be possible to break AES-256 in your clients scenario. Full key recovery is out the picture even with a terrible implementation, unless there's a weak way that key is stored. Finding the AES key on the computer itself (encrypted using more vulnerable techniques) is your only shot in hell.