New job schedule needs to wait for the old schedule's next run time before becoming effective

[andylewise]

With the current job's mechanism, when we change the schedule, the existing task registered with the old schedule is still waiting. Only at the next run time of the old schedule, the task is executed and then the new schedule will take effect.
It may be just fine for shorter interval jobs, but it can be a problem for longer interval jobs (daily/weekly).