So I got it working, but it's a bit weird.
First of all, had to set the sensitivity to 1, which is the highest. Default is 11. Second, I only want it to trigger if we're changing states. That is, from on to off, not just opening and closing the door. So the solution is to create a binary sensor with delay_on and delay_off so that it only changes states when you go to the on or off state for that length of time.
My initial idea was 5 seconds on, 5 off, which eliminates the door opening and such. The only thing to be mindful of is that the default timeout is 60 (65?) seconds, so once it reads, it won't trip again until the timeout expires. Translates to if you turn the dryer on for 10 seconds and then off, you don't get the off state to trigger until 60 seconds after it turned on because the sensor doesn't poll that often.
It's a complete bodge job of a hole, but I took mine, put a USB UART connector in there, and jumpered the pins so I can have serial console access on it.