After lots of research and actually digging through the Netbeans source, the only way to go about this would be to fork a version of Netbeans where you add this functionality yourself, but this is not possible in any release of Netbeans at the time of this post.
I spent multiple days searching for an answer where people suggested the wrong things (like setting up variables in file templates instead of code templates, or the doc listing the file template variables under "code templates", etc.) or just never got an answer, so for all of the other people like me searching for this, it's just sadly not possible at the moment.
