Ok, after figuring a lot of stuff out here are some notes. It seems that it's not really needed to change the mysql password of user ispconfig. It's even unwise, so I'd suggest to leave it be and rather use the new password on the new system for anything you have migrated.
Don't forget to set quota as your new system has no quota ...yet
I did a lot of mysql stuff because my DNS entries had to be updated in bulk. I edited all the entries in dbispconfig's dns_rr table, and then all I had to do was to click 'edit' and then 'save' for each zone. Saved quite a lot of time there. I also had to do this for ipv6 addresses.
You know, the biggest problem is that you might overlook something. The transition to a new system isn't exactly fun, but it's well to do. So if anyone has questions, just drop them in this thread.