Toby, When the dryer is in auto dry, once the timer starts advancing, does it ever pause in its advance? The reason I ask is because if it is cycling on the high limit thermostat, that does not pause the timer. When Maytag offered some time-temp auto dry models in the HOH design, long exhaust runs would cause the high limit thermostat to cycle the heat, but not the dryer timer so they would complete the cycle with damp laundry. That is why your machine is suspected of cycling on the high limit thermostat. This is also why Hamilton dryers did not have an automatically resetting high limit thermostat. If it tripped, a service tech had to reset it and before doing so had to find the reason. Often it was because people were only cleaning the top of the lint catcher and not the lower portion. Some older dryers used a piece of solder that actually melted in an overheating situation and that disabled the dryer but good until the cause was found, but that was when dryers operated at much higher temperatures.
I guess you have checked for a bird's nest, dead animal or other obstruction at or just inside the vent opening. Have you taken apart the blower housing? Things can fall down inside the filter housing and partially block the airflow which could cause the hi limit to trip or something could crawl into the vent run and die there, although that is generally smelly pretty fast. Certain fabric softeners can cause a lot of lint to buildup on the blower blades, too. A quick test John showed me is to lift the lint filter lid and partially pull out the lint screen while the dryer is operating and feel if there is strong suction.
Another big question: Have you checked the lint screen to see if the screen is clogged with fabric softener? This can be a big problem if anyone has used fabric softener sheets in the dryer. The screens can get so clogged that water will not even go through them. They have to be washed with a strong cleaner like Knight's Spray 9, a mild brush and hot water to break that film. If you have partial clogging of the filter, that could be tripping the high limit thermostat.