That's a lot of great, rational, decisions for how to set up those rotations.
On the scheduling front, how do you decide which engineers will be working which shifts?
Have you considered scheduling solutions like
https://oncallscheduler.com? It makes the scheduling automated, fair, stable, and gives the rotation members control over when they work. It writes schedules into PagerDuty, and gets the times when people work onto their calendars.