I have been living with this for decades and never completely eliminated it. When I was younger, fitter (dafter), I tried to blitz it from existence. This did not have the dramatic effect I thought it should. As you say it is a minor nuisance, having little or no effect on crops. Latterly I have been pulling it out whenever I see it, with as much root as I can get or cutting it as deep as I can with a kitchen knife. In answer to your question ” when is the optimum time “, I don`t think it matters. What I can tell you is; that with persistence it is possible to virtually eliminate it and this can be achieved within a human lifespan.
Pete