I like the lasagna garden method which you might already know is to layer organic materials which builds the soil and also smothers the grass and weeds underneath. my understanding is that tilling will just bring up dormant weed seeds which will then sprout. also if you till when the soil is wet and muddy it will clump and that ruins the soil structure. i also have heavy clay, the key is to keep adding organic material as you have been doing, mulch, and also only work the soil (planting) when the soil is slightly moist but not wet and clumpy, it should be crumbly. there are a lot of good properties to clay i had to learn that and never try to dig when it's dry it will break your arms and tools. i don't know about the cover crop, but if you have a farm store nearby or co-op they could prolly tell you about a cover crop. clover?

We recently relocated to Knoxville area from CNY.... Where I had wonderful lush gardens - quite the green thumb I had - or at least I thought! Gardening in TN is quite a challenge - or at least at our residence. Our house had been abandoned for few years and the lawn and gardens were a mess. We have heavy clay soil as you seem to have, and lots of trees with lots of leaves. The lawn - well there was not much lawn... More like lots brown patches! After two years, the lawn is so much better... Just the mowing (and resulting benefits from the 'clippings' has helped... And we have seeded and seeded. We started a small vegetable/herb garden - but we built raised bed and filled with store bought soil due to clay... Anyways... What I have found to work so far is adding into soil (well clay) any organic matter feasible - like chopped up leaves, grass cuttings, coffee grinds, ground egg shells, etc. I do not use food scraps because we have lots of squirrels and a resident opossum! I have even bought bags of lime and dumped onto lawn ... Wherever.... My herbs seem to grow the best here. So what I would suggest you start adding organics into soil... If too clumpy to use tiller, use hoe... And yes, plant any plant that will grow right now... Even if you plan to till in - herbs, cover, clover (we have lots of clover in our lawn - which is fine w me - anything green!) and greens (like edible ones... They grew well in my garden last year)... I am certainly not expert here, just sharing what I found has worked so far... And am certainly seeking continued support and advice! Good Luck!

Maybe you should consider starting your greens in a container?

I raked one row of the old growth back and planted some onions and covered with leaves just before we had a big snow/ice storm. Now the snow has melted but it is really wet. Hopefully in a few days I can rake the rest of it. I am sure I will have to till it some to work in some organic matter. I have tomatoes, peppers, and cabbage started indoors. I am going to get some straw bales and try planting a few things in there too. A lot of experimentation going on and hopefully my garden will be a little better this year.

Good Luck Rebecca! A local gardener recommended adding in sand to garden area...to help break up clay... Which I did last year... Did seem to help!

Sand added to clay makes concrete! Only add organic matter, like shreaded leaves and organic grass clippings. I cover the spring weeds with cardboard and top with home made compost mixed with soil conditioner, bunny manure and whatever I can afford. A compost pile is your best bet. Tilling can also damage your soil, so the lasagna method is the easiest and most earth friendly, though you can spend a lot to build it up if you don't make enough compost.

One other way to eliminate weeds if you have time is to sterilize the soil using plastic. I think they call it solarization. You basically just anchor the plastic down on top of the area you want to eliminate the weed seeds. You want to do it during a time when the temps will stay above 80 degrees. Just do a search on solarization and I'm sure you will find more info. It takes weeks to work, but it really gets rid of the weed seeds.