Personally if you are not wanting to use chemicals or tilling/discing methods, you may want to consider controlled burns. Also you should incorporate not only plants that suppress's weeds and grasses but reduce the acidity of the soil (lime). Then repeat the cycle for a few years to illiminate or reduce weeds. Just be extremely careful with controlled burns. Personally think the summer fowling (discing/tilling) is much safer and more productive. I have seen the evidence of controlled burns getting out of control along M33.