Encrypt a file for multiple persons with different keys?
Now the condition is, that each employee has different key material
solve the above problem, without the overhead for the additional headers

Based on your requirements - you must have the different key material for each user... which obviously has to be stored somewhere.  You don't want it in headers ... so it either needs to be in a different file / database, or in the meta-data.
We had a similar problem which we solved using Extended File Attributes instead of additional headers.  The symmetric file key was encrypted for each authorized recipient using the recipients RSA Public Key and the result was stored in the file meta-data.
https://en.wikipedia.org/wiki/Extended_file_attributes
Some filesystems have default limits on the amount of meta-data you can store. You may need to configure those.