It's not as hard as you think to get rid of. It does take 3 seasons though, so it's a long process...

You basically just have to starve the rhizome and you can do it without chemicals even. You wait until the shoots start developing leaves and cut them all down, then just keep repeating that process. If your lucky the rhizome will start rotting by year 2, but it generally takes 3 years. You need to ensure it spends as much energy as possible shooting and don't let it get any sunlight from leaves.