... due to our policies, I'm not allowed to use crontab where I can configure it.
Clearly, there must be some reason for this policy, though it is not obvious what it is. Any alternative scheme could potentially fall foul of the same reasoning that caused them to forbid cron. (Certainly, some of the alternatives proposed above are likely to be worse than cron.)
The best thing to do is to ask the people who set this policy to tell you the approved way to schedule a job. Or at least ask them to explain why the use of cron is forbidden so that you have some idea what to avoid in any alternative scheme you come up with.
(OK, it is possible that the policy is a stupid knee-jerk reaction to some problem in the past. But, you still need to understand what the problem was ...)