It sounds like the cleanup doesn’t run all the way through. See if there is a „update-assets“ folder in the root of your shop and rename it (to update-assets-bak or something similar). As long as this folder is present the maintenance screen is being displayed.
If that fixes your problem and your shop runs fine, you can delete the folder lateron.
Nope, already checked for that and also for maintenance.html, since i found somewhere that this file might stay behind, but there isn’t one.
The strange thing is that the folder production_201803081536 is not even in var/cache/, before the update starts. There is a folder with some other date, but not with this one. Then all of the sudden, this folder comes up and it keeps coming back over and over, even though i delete it manually.