Apple Mail: Move thousands of locally stored mails to IMAP accounts
Whats the most efficient way to migrate such a large local archive to a single IMAP-Account?


Unfortunately, the most efficient way to do this is to migrate from one IMAP server to another.  I say unfortunately, because this is something that happens at the server level and not via the user.  

In all of the migrations I've been involved with (all from something to Exchange), we kept migration to a minimum and archived everything.  That archive remained "online" for reference only (it didn't accept new mail) and new folders couldn't be created.  After a number of years (3, I believe) it went to permanent archive in which we took it offline and only went to it if there was reason to do so (like legal subpoena).

In the end, migration was simply too costly (time, labor, efficiency, dollars) so it's rarely done.

In your case, unless you have access to the back end of the servers, your service providers are not likely at all to accommodate the request.  So, unfortunately, getting those mails over to your new server is going to be a manual process.

With all that said, my recommendation is to move away from the (dated) IMAP severs and look at Exchange.  It's the gold standard.  You can get a hosted Exchange account from Microsoft for $8 per user per month and it's a much better solution than pretty much anything else offered.