You could try cardboard with wood chips or leaves on top. I use that between my fruit bushes and it lasts a season. Needs topping up every winter and you need to get rid of all perennial weeds before putting it down.

I do what floral does, but haven't bothered to remove or kill perennials first. The cardboard and mulch do that. Or am I in for a big surprise?

agree with the other two, but that limits you to planting relatively large plants through the cardboard. Also, high temp underneath and it prevents weeds from germinating. You want, ideally, to have them germinate and then kill them. all the while doing no-dig to avoid new weed seeds.

Since I collect leaf bags, I prefer to use the paper bags for mulching (held down by bricks). they disappear early enough in the season that there is a massive start of weeds sometimes in June. But it is too late and the main crop smothers them. Specially collards and squash. I also have two beds where I planted clover three years ago, and those are nearly weed-free, but I can only use transplants in there. Other low ground covers, I assume, will work similarly.

Bindweed is my main perennial weed. It will find the joints in the cardboard even if it has to travel several feet to find them.

A 3000sq ft garden is very large to not have daily access to. Would help to know what you are growing?

I also use cardboard or layers of newspapers held down by mulch. You could use a salt-hay mulch where the plants are growing.

Bindweed, bittersweet, etc. are some tough weeds no doubt. Keep in mind that weed seeds can survive for 40yrs. below the soil so that is a good reason not to till if you are or have been turning the soil.

A cover crop is something you should also consider. You may well end up with a combination of control methods.

I know some farmers grow a cover crop like a Alfalfa then use roundup on it when it gets about 3ft, give it a couple days to die then roll it flat to use as a mulch. Then plant their seeds right thru this mulch. This is a "No Till" method used by some farmers.

Just some ideas - not suggesting you should use roundup. I don't like landscape fabric cuz weeds grow thru it then the fabric tears and will live in the soil longer than we will be on this planet.

At least the newspaper or cardboard will feed the soil, which is what you want - feed the soil, the soil will feed your plants.

Good Luck

i would also go with cardboard and mulch. am doing this in my petite garden, works well.

Would a couple of fast growing pumpkins shade enough of the soil to help suppress the weeds.?

Our two new asparagus beds needed some heavy weeding a couple of times before we added mulch. Right now in late September, there is Creeping Jenny trying to invade the bed from the edges. All my garden beds are surrounded by lawn. The bed that contains smaller plants did pretty well this year. Last year I edged it at an angle since some spreading weed roots don't like it when they hit air. Also, the riding lawn mower can get closer to the bed. The other thing I do which might not be possible for your large garden, is to edge some critical beds with wet newspapers covered with fresh grass clippings. The mower wheels can ride over this. There's a large market garden near us that plants an edging of flowers about 3-6' deep. Some self seed. It's sort of a wild area that is mostly flowers. My vegetable beds don't need much weeding once plants get established. I mulch potato bed after the first hilling with dirt, with a thick layer of straw. After I plant my garlic later this month, that bed will be covered with straw. The garlic grows up through the straw but rarely any weeds.

When I had a large planting of sweet corn, I liked running a mini tiller between the rows. Winter squash does a good job of growing and shading out weeds but after the season, the creeping weeds move in. I have to cover bed with black plastic in the spring to kill the creeping Jenny which then makes it easier to remove with a spading fork.

I follow some of the local market farmers on facebook. When I look at their photos of long neat rows I see a lot of straw mulch used between the rows. In my high tunnel I put down wet newspapers covered with grass clippings to keep walkways mostly weed free. I also see the farmers using a lot of black landscape fabric for tomato beds.

Landscape Fabric under tomatoes, peppers, melons, zucchini and things you plant as plants. Lots of hay and straw around onions, potatoes, beans etc. Preen around radish, lettuce and quick crops AFTER the crop has sprouted. Or a combination of all 3.