Do Nursing Management positions offer the 3 day 12 hour schedules?

Management is very rarely an hourly position. It's salaried, and you're there until the work is done. Most of the managers in my department work minimum 50, some up to 60 hours per week without additional compensation. So if you're hoping to work management as a three day a week 12 hour shift, it's not likely going to happen.

Our managers are all five days a week with alternating on call weekends.

Most nurses I know don't want to touch managers jobs because of the loss of paid overtime!

Not in my experience, no.