Mounting Contact Sensors on Door Molding

I am installing the Ring Security Pro system this weekend, and the doors in my home all have Molding surrounding the door as shown in the attached photos. The 2nd Gen Contact Sensor does not have a flat surface to mount on except for the narrow portion of the door frame, which is too narrow to permit the Contact Sensor to be mounted without overlapping the door. Has anyone had this same problem, and how did you resolve it so the Contact Sensors can be mounted on the Molding, which is not flat? Thanks in advance for your help with this problem.