Note to myself: when software updates are downloaded in CCMCache, but not installed afterwards, have a look at this (short) blogpost.
When the message "No current service window available to run updates assignment with time required = 1" is displayed in Updatesdeployment.log and/or "Past due - will be installed" within Software Center, just look no further. This is definitely a conflict between the software update deadline and a maintenance window configured on the collection. After changing the behavior of software updates or the service window, all will be fine after all.
Another day, another challenge!
Source: System Center Central
Update: In the end it was a boundary issue after all. No service window was found on collections, but it can be the issue also.