What is the most logical next event?

How to get rid of japanese knotweed
Cut down and remove the canes.
Japanese knotweed will not regrow from cut canes, so it's important to trim down as many as you can. Use loppers to cut off the canes as close to the ground as possible, then remove the cut pieces from your lawn or garden.
Apply glyphosate weedkiller. Glyphosate weedkiller, like roundup, can help you get rid of japanese knotweed.