The important thing is, I don't need all the data istelf to be decrypted (save for one file)!
My Problem: I have an AES-256 encrypted zip archive and I additionally have all the files that are in that archive in their unencrypted form, except for one that I need to recover. Is there a way to somehow recover that password by comparing the encrypted and unencrypted versions of the remaining files? Or any other way to recover that one last file? The password was randomly generated with more than 16 characters (and lost to time, eventually), so simple brute force isn't an option for me.
What you are trying to do is called a "Known plain-text attack" on AES-256. Unfortunately for you, there is no known way to achieve such an attack on AES-256 with feasible computing resources.
See Why is AES resistant to known-plaintext attacks. Here are some estimates of how ridiculously much computation power is needed to brute force AES
If any successful attack on AES-256 were discovered it would cause headlines far outside the world of computing; much of the world is heavily dependent on the security of AES-256.