It occurs to me that the Pi-with-watchdog-script isn't the only way you could make this work. You could also use some type of cellular modem device capable of receiving text messages. If the router was stuck, you could send a text message to the watchdog that would cause it to engage the open drain output for 2 seconds and reply with an acknowledgement.

I might see if I can come up with a way to connect an Adafruit FONA 3G to the Pi.