It seems to me that your shop does not allow cron for a reason. Could it be that they have a standard tool/package for scheduling of this type? Perhaps, something like UC4, TWS (Tivoli Workload Scheduler, AKA: Maestro), AutoSys, Control-M, CA-7, etc.

These are very powerful tools; you might be better served looking into what your shop uses and working with the necessary team(s) to implement that way.