We've removed all permissions from all users other than the owner. Result: notifications are lost. Test orders and regular orders do not generate order notifications.
Turn the permissions back on, but leaving store permissions off except owner: order notifications go out, but are still being emailed to the previous site owner who doesn't have permissions set to access store information.
I've scoured forums, and tried several things. Why is it so difficult to get help? I've been using squarespace for 15 years and have never had a problem like this.