i dont see anyone mentioning that the traditional use of knotweed is to treat constipation.
i had a big patch and pulled a lot of it, just left it to dry where it fell. my dog started grabbing the nice "sticks" when it dried. he got a case of diarrhea that was hellacious.
i had some luck pouring a little gas on the recurring shoots and lighting them on fire.
but mostly the chickens have attacked it, and even tho there is still a source on the other side of the fence, i dont see it in my yard.
i think a weed torch would work well, just make sure you hit at the roots hard.