We eventually brute-forced it by making a matrix of volumes and schedule types, so we could very quickly respond with what the load calculation of staff was vs the number schedules that would be required to actually cover based on minimum staffing levels.
So if the volume was ~100000 calls per month and the coverage was 5 days a week, we’d be able to return our numbers very quickly.
I moved on to other things, but that remained in on the backburner for me. I eventually made some contacts with actuaries and was planning to work with them to figure it out since they specialize in equations with massive numbers of variables, but my role changed within the company and I am no longer responsible for having to justify to financial planners why their calculated number of FTEs is so much lower than what we need to actually meet the service levels 🙂