We want staff to get the email reports just from the groups they oversee.

Under Groups & Events > Organization are coach and staff areas. These were designed to do exactly what you want. Add in the people who oversee groups as coaches, then assign the groups underneath them. They will get the emails just from these groups. If you have another level above that, then use the staff area and assign coaches to the staff. Staff also get the emails of all groups underneath their coaches.

Then, under Groups & Events > Settings > Basic, remove the email addresses from under "Attendance/Reports." All emails listed there will get all attendance reports no matter what.

In this area under "Leadership Titles," you are also able to customize the names you give to leaders, coaches, and area leaders (staff).