Nice answers here.
In reply to the original question I would ask one of my own, why not grow some plants in whatever manure/compost mulch you may apply? There is no need to wait for everything to fizzle out underneath, grass and dandelions can be rotting away while your squashes, leeks, beans etc are growing on top. You need a minimum 4 inches organic matter for this to work though. Then, as you say, to keep removing any weeds poking through until their roots are exhausted.
Good growing!