The only thing that I can think of is using the Task/Appointment module to add private tasks to each employee. I don’t see a way in the UI to set up a recurring task, but I’m wondering if maybe an escalation or workflow can be created to add tasks automatically daily, weekly, etc.

A bit of an initial setting but may do the trick.

you can create a dummy item per employee (yes, that's a bit stargange but you can create the product as ‘security check + <employee id>’) , set the default employee on each one. now a contract with the items and a cycle pm can generate the activities (with a checklist) on a regular basis.

Another option is to create a contract with one item and a pm cycle, generate the call on a regular basis and have an escalation/process flow that will add an activity (with a checklist) per employee.

   not ideal but just a thought...