How would I get a cron job to run every 72 minutes? Or some not so pretty number like that?
You'll need to set exactly 20 tasks for this - i.e. set one at 00:00, next one at 01:12, next one at 02:24, etc.
20 iterations make a full day.
Unfortunately, this is the only way to do it, as cron tasks are set up in a fixed schedule beforehand instead of being run, say, "after X minutes the last task was executed".