Can files be 'over-encrypted'?
With the current computers this would not take so much time. There is a high chance that reading / writing the files or sending the files over the network will take more time. If you've got trash like the McAfee virusscanner installed on either PC then that will take much more time as it will try and scan the files in the zip file at lower than 1 MiB/s.

Passwords are generally not very strong, while encryption using a hybrid cryptosystem such as PGP using an RSA public key is very strong. The password based encryption (PBE) is made worse as you're using SHA-256 instead of a password based key derivation function (or PBKDF). So an additional encryption would indeed not be a bad idea. In general you could do without the password encryption, but not without the PGP encryption the way you write it down. Note that the PGP encryption is also protecting the file names; it could be that the file names are sensitive too.

Even when using PGP you should check if you're not vulnerable against Bleichenbacher attacks, padding oracle attacks. This would mainly a problem if you automate the decryption when the files are received. Protection should also be in placed to disallow changes of the plaintext, for instance by signing the .zip file.

So I don't think you're over encrypting, rather the opposite. That said, performing encryption right once makes more sense than performing it badly twice.