You seem well on top of weeds, it sounds from what you say that there is little or no couch grass, the only weed likely to be a continuing problem. But with all that leafmould and cardboard, then manure, it should be fine.
Leave the cardboard in place, with manure on top, it slowly rots in situ, Plant potatoes in the manure, I don’t think you need plastic. Just grow a courgette or two! Or winter squash. Enjoy keeping on top of the few bindweed!