Thanks Rob for that input!
I was able to solve my issue now by changing the maxWait time for the job executor form the default value of ‘60000’ to ‘5000’, i.e. (as far as I understood it), now at least every 5 seconds it is checked whether a job is due.
(Side note: This seems to be fine in our quite special use case with rather short timers that should be executed quickly after being due - but I noted that this change caused rather heavy CPU usage. So be careful if you try to use this in production use.)