Diagnosis
You've nailed it. Those two metal strips on the back wall of the drum are the moisture sensors. They work by sensing the tiny electrical conductivity change when wet clothes touch them. Fabric softener residue, lint, and general grime insulate them, making them 'think' the clothes are dry long before they actually are.
How to Fix It
Unplug the dryer. Use a bit of rubbing alcohol (isopropyl alcohol) on a clean rag or paper towel—it evaporates quickly and won't leave residue. Gently scrub the face of both metal sensor strips until they're shiny and clean. You can also use a mild abrasive like a melamine foam eraser (e.g., Mr. Clean Magic Eraser) lightly dampened with water. Avoid harsh chemicals or steel wool.
If That Didn't Work
If the sensors are clean and auto-dry is still cutting cycles short, the sensor wiring might have a loose connection where it routes out of the drum, or the control board's sensor circuit could be faulty. But that's far less likely than simple grime.
Heads Up
Clean those sensors every few months if you use dryer sheets or liquid softener. For the most accurate auto-dry cycles, also make sure you're not overloading the drum—clothes need to tumble freely to make consistent contact with the sensors.