One of the linked articles suggests not cutting the growth back to the ground unless you are ready to hit it with the chemicals or dig out the roots (as the plant will then focus its energy on root growth, which is the thing you have to get rid of with JKW).

Always thought that I was fairly safe from the stuff but I noticed that there is some growing in the front of one of the nice old apartment blocks opposite FH Sainsburys - and I live about 100 metres up the hill from there.