I've had some success with Lasagna Gardening....putting stirps of newspaper down to keep grass & weeds from growing. Lasagna Gardening aka Lazy Mans Gardening Nothing can grow without light or too much heat.

Fori, crabgrass is pretty evil in my book. If I were to cover it with newspaper and mulch, wouldn't I have to at some point remove the dead remnants of the crabgrass? Wouldn't leftover seeds spring back to life if and when the topping gets wet or removed?

In case I wasn't clear in my OP, this isn't just a profusion of weeds, it's a solid, dense layer of crabgrass.

How about planting something that will eventually choke it out?

https://homeguides.sfgate.com/thick-ground-cover-thwart-crabgrass-90983.html

Deeply established crabgrass is almost impossible to kill because the roots are so tough. Even the evil weed killers require multiple treatments. Short of burning it out I can't imagine you'll produce enough heat to fully kill it with plastic of any color. The top will die but those roots will live on. My vote is hire it out if you can because it's a very specific, contained area, The most efficient way for someone to do it would be to dig out the entire strip about 8" or more if the roots have gone deeper then fill in with new soil.

The only luck I’ve had was digging it out before the lasagna method. I then planted ground cover, and so far so good (hell strip).

It might be worth seeing if you could hire someone? I will next time. My poor back.

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“Crabgrass can grow on bowling balls in airless rooms, and there is no known way to kill it that does not involve nuclear weapons.”

~ Dave Barry

Just make sure you don’t trade one invasive problem for another. Think of kudzu.

Dave Barry is spot on.

DLM and Jinx, I'm thinking you're spot on and I just need to hire someone to dig that beast out.

Dee, unfortunately there's no room for anything else. The crabgrass has won Round 1.

There will always be more seeds unless you're on the ISS.

Here me out before you throw things at me. :) With such a small patch I'd use Roundup. Any other weed a garden claw will get it in five minutes. Wear plastic disposable gloves, and buy a small bottle of the condensed stuff. Not pre-made. I use a regular spray bottle like you'd use for ironing, and I make it super strong. Dead. Do it on a warm sunny day. It dries within minutes.

If it's a windy day get a piece of cardboard and and hold it next to the weeds so any excess spray doesn't blow away.

We run into this problem all the time when trying to restore and maintain prairie plantings. It's not just the issue of killing the grass that is there (which you have to kill ALL the roots to accomplish) it's also the problem of the seedbed, which is full of dormant seeds, which any type of tilling can bring up. This is why folks like fire, it is hot enough to kill the seedbed. That's why you would have the soil removal suggestion, to take the seeds with it. Annual weeds are easily killed by fire but I don't know about crabgrass. I suspect it is killed but still has some fight left in it for coming back to some degree.

Are you planning on replacing it with grass? If so, short of burning, there are three approaches, all with pros and cons. 1. Before the crabgrass sets seed, treat the area with a strong (40% solution) grass or brush killer. I think what they sell is either glyphosate or 2-4-D. Both of these compounds, while toxic, will break down in a short period of time to non-toxic constituents. Wear protective clothing, a face mask and goggles and keep everyone including pets out of there for at least a few days. That's all that's required but I would wait two weeks before I went romping in the area. Then, when the weed killer has broken down, you can reseed. You will still have to spot treat crabgrass weeds for years to come, but it will begin to get a handle on it and that method doesn't disturb the seedbed.

2. Kill the grass with either plastic or weed killer, then when it has broken down, remove the top layer and replace with soil. I'd then sod it, because that has soil too. But you could also seed. Then spot treat weeds for all eternity.

3. Kill the grass some way, then heavily mulch and plant the grass over the mulch. You will still have weeds popping up but you will have avoided disturbing the seedbed.

If it were me, I'd kill the grass and then sod.

Pink, no plan to replace with grass. No grass at my house, period. It's a small backyard, mostly deck and Mexican pavers. I have a strip that runs between the pavers and a planter box next to the fence. I originally had irregularly spaced flagstone in the strip with woolly thyme growing in the spaces. It was good. Until it wasn't. A little neglect eventually became solid crabgrass.

Can you post a photo perhaps? Are we talking a small space that you want to replace the crabgrass with a ground cover? And are flagstones involved? Flagstones are difficult, I had two patios at work I was charged with keeping crabgrass free, and it's tough because the seeds and roots can easily hide in the cracks and are very difficult to dislodge without disturbing the setting of the flagstones, which then sets you up for further invasion by weeds. They can hide there from a cover and mulch and then spring back up as soon as you remove the cover, even if the grass in the more open areas has been killed. It's also hard to pry them out by hand. This is a case where I would judiciously use a bit of spot treatment with the concentrated weed killer, one that breaks down. The reason I would do that is because it is a spot treatment and the toxic constituents are unlikely to come into contact with any other life forms other than some soil microbiota, but that can bounce back. Again, using all precautions and keeping away from the area for the requisite time for the pesticide to break down . . . must be followed up by vigilant weed removal over time . . . which is also why weed killers get used in certain spots, the difficulty of keeping up with the manual removal methods . . . again, follow precautions and plan to mitigate any drift to other organisms or areas.

On the flip side, in a small area, one can devote oneself to manual removal and have success . . . if one had the time, back and knees.

What I would do if you don't want to use chemicals is, pull it all out. Plant Dwarf Mondo in it's place. Dwarf Mondo sort of looks like grass except it doesn't get very tall (you may already know this). It's an evergreen, is slow growing and requires almost no work and thrives in almost all soils.. It will take two or three years for the little clumps to fill out to choke out all or any recurring crabgrass. There maybe a little crabgrass weeding on your part till the Dwarf Mondo does a full cover. You can step on it as it's pretty hardy. I Love Dwarf Mondo and did a small curve of it in sons tiny yard where nothing would grow properly under/along the roof overhang.

ETA: for zones 7 - 10.

It will look like this till it fills in.

The photo below is almost filled in.

Here it is filled in.

If you want grass in the area, try putting in zoysia plugs. We have patches of zoysia in our lawn and it spreads itself and gets very dense...so dense that it has no weeds. The only thing is, it will turn beige in the winter and not green up until it gets warm again, but I don't mind it at all. Very drought tolerant, it will stay green all summer though the regular lawn will turn brown. What I love about it is the blade grow at an angle creating a cushion-y feel when you walk on it.

https://www.pennington.com/all-products/grass-seed/resources/all-you-need-to-know-about-zoysia-grass