This doesn't answer your question but my Gdrive is a mess and I'm only one person. Typically I download the the contents on an annual basis in zip files, extract them to a Month/Year named folder on a portable drive and start fresh with a clean Gdrive until the next time it gets out of hand.
I would think Downloading first then using parsing tools locally would make things much easier to organize than doing it through Googles front end.
After thinking a bit more about it, what you probably need to do is make a requirement for all internal emails to be CC'd to a central address then use that address to download and or synchronize itself to an offline drive where perma links can be issued.
I missed the part about people sharing from their own personal gdrives, this will surely cause problems with broken links when they leave the company and restrict access, Google drive allows multiple users to upload files to a shared folder then edit them but I don't know if there is a seamless method to create a new file or document in a shared folder.
I think what you are asking for is a solution to your problems that something like moving over to SLACK might do.
but if you are set on using emails and Gdrive only then...
I'm pretty sure there is literally is an option to download, and if you have a PC dedicated to doing this, you can use chrome and google offline drive sync to clone a google drive to a desktop and automate the process.
Not to get too far into it but what you need to do if your plan on sticking with google is have a single system/google account share out access to folders created on it that are specific to each employee. I think you may have done this already.
Then it should be a matter of following these steps.
https://support.google.com/drive/answer/2375012?hl=en&co=GEN...
if you want to chat then feel free to drop me a line: haroun@dala.ai - would love to exchange notes/thoughts.