Maytag gas dryer doesn't stay lit unless hi-limit is moved

Our Maytag MDG9700A dryer doesn’t stay lit. After starting, the gas ignites for just a few seconds and then shuts off. Most forum answers tend to point to air flow or the coils but it continues to light (and then shut off) with each cycle and the dryer is disconnected from the vent pipe (and airflow appears to be strong out the back with pulsing if there are clothes in the dryer as they tumble over the vent but I suspect that has to be normal). The resistance values across the posts in the coils stay in normal range with repeated starts. The flame stays lit IF I remove the hi-limit switch from the duct or disconnect the wires and hold the ends together (of course it stops as soon as I pull them apart). However, the high limit switch itself is closed whenever I test it, even when holding it over the flame on our stove - and the flame in the dryer duct isn’t on very long before it shuts off. I wouldn’t hesitate to replace the hi-limit switch but I’ve read several other posts that say they are experiencing the same thing and it still doesn’t work after replacing the switch and I haven’t been able to catch it in an open state yet. The thermistor values appear to be within range as well, smoothly rising and falling with temperature changes. Once in awhile the clothes are warm at the end of cycle but most of the time they basically air dry for a few hours. Changing cycles and other options don’t make a difference. Without wanting to order twice, do I need to order a hi-limit switch and coils at the same time and what are the chances that the thermistor has a problem? Or am I missing something else? The dryer is at least 5 years old and is used daily.
Thanks!