I've not had to shift rosebay willowherb roots, but they're pretty big, and it's a PITA because it seeds so vigorously rather than spreading by root, so I wonder why you don't dig it out?
If it's because the ground is hard (not sure which side of the great rainfall divide you are), I can't see why you don't go for the cardboard. Though it seems a bit of a f*g moving the soil on and off it - or do you mulch the cardboard in?
Given that black plastic will even kill off couch grass (bindweed, sadly, is a different matter, I swear it survives for decades in the dark) I think anything excluding the light will help kill it, though as there's a lot of energy in those big roots it might take a while.
Adrian