I claim no familiarity with the likes of bindweed but as to controlling invasions of creeping buttercup & couch, i can assert that a thick layer of straw will do the trick. It acts as a 'light excluder' depriving the weeds of light, without which they cannot thrive. The straw does need to be laid down thickly though, at the very least a 6" layer. It will settle down within a few days, and you may consider topping it up again.
I'm on very heavy clay which varies between being so claggy you can't work it to setting as hard as cement when dry - using straw as a mulch (but not exclusively) keeps the soil friable enough to plant into without the aid of a jackhammer. I also apply it to the edges of the potager and all paths, underlaid with corregated cardboard. Saves on having clay stick to the soles of my shoes and absolutely stops weeds growing in the pathways when you cover right up to the edges. I also applied it over winter to keep the soil covered. There's nothing weeds enjoy more than bare earth so i'll continue with this method and perhaps may try a green manure next winter to see the difference. That will give the added advantage of more nitrogen into the soil in readiness for spring planting. The cold/frost will kill it off nicely so i won't need to dig it in. I follow a no-dig approach to preserve the soil structure as best i can, and i can't see the sense to encouraging earthworms if you're intent on macerating them with a rotovator.
This is the first year of gardening on clay and i can compare my plantings, which are well under way, while my neighbours still await the clay to be dry enough to work. There is great value in mulching with whatever organic matter you can obtain. This first year, starting with a substantial covering of couch and creeping buttercup, I layered with cardboard, straw, sheep/cow muck, coffee grounds, municipal shredded compost, vermicastings, ash and leaves. I'm pleased with the improved condition and see no reason for it not to continue as the organic content increases over time. There's no such thing as too much organic material for a healthy, productive garden.