Ring Groups can have a Class of Service:
Enter the Class of Service to use by all Ring Group members when the system is in Day service mode. If left blank, the Ring Group uses the Day COS of the first programmed member.
I think you'll want Display ANI/ISDN Calling Number Only set to "Yes" but someone may need to correct me on that COS setting.
I would set up a COS for Ring Groups rather than modify the COS of the first number, that way you can reuse it for future groups.