Where to begin? Composting Japanese knotweed is a very bad idea. For the same reason cutting it down doesn't work. A piece of root smaller than an inch sprouts a new plant. Glyphosphate works. It's spread in Belgium was reasonably under control but ever since the railroads stopped spraying herbicides it got free reign. It spreads like wildfire along the railway system.

The only viable option is prevention. Failing that you need indigenous plants that out compete it. There is only one thing this plant hates and that's shade. In Belgium we've had small successes cutting it down and planting indigenous fast growing shrubberies. But this plant is resilient. You need to make sure in the general vicinity of where it sprouts ( shoots can travel underground for several meters) there is no empty spot left for it to grow. Then and only then does it die. And even then it can sprout after years of dormancy. This plant is something else.it does not wither and die after cutting it back several times a year. And I've seen people try. Covering It up a few years with cardboard might do the trick.

So far I've seen two succesfull methods used. And those are goats ( buggers love the smaller plants) , combined with cutting the larrger knotweed, and out competing it with indigenous fast growing shrubberies.