I still have the problem that the databases have become too large. Some tables are so large that I cannot perform DB optimization on them. There is simply not enough storage space for this.
I have now tested a different approach with a smaller test server. Backup (dump) the database, drop the database and re-import the backup.
This worked well and saved about 60% disk space! Incredible! I will have to do the same with the large databases, otherwise I will soon run out of disk space.
Unfortunately, this will take a lot of time. A lot! And with a lot I mean probably around 2 days.