It's not so much that they eat the plants ( although they love to peck ripe tomatoes ) but chickens scratch through the dirt looking for food and can do serious damage to plant roots .

Try guineas .

Round up when it is warm and cover the area with black root block cloth when its cool to deprive it of light. or
...

I used Round Up for years but there's a lot of debate right now about certain chemicals being left in garden soil . You can put sheets of clear plastic down and the heat will kill all the roots / weed seeds / worms / beneficial nematodes and bacteria / etc . You'll have an essentially sterile plot of land that you'll need to inoculate with all the "good" bugs .

I think napalm leaves an oily residue . Might taste funny on turnip greens .

What kind of grass ?

Read up on MSMA weed killer. It's good for a lot grasses and broadleafs. As others said, it would be best to identify
what you have, before choosing how to control it. The black cloth stuff works pretty good, but I've seen stuff grow through it.

bermuda, crab, and st augustine. The crab is easy to pull. The bermuda aint.

Burn it off then break it up

MSMA works really well on Bahaia and San Augustine but I believe it's banned now . If you can find it , try 10% vinegar instead of the 5% from grocery stores . Bermuda sends out runners underneath the surface so you might need to kill all of it in the area or sink a 6-8" barrier around the garden .

That too . Be sure and get all the roots .

Just so y'all know, Glyphosate [roundup] takes several treatments to kill the rhizomes on Bermuda. This works way better for controlling monocot [grassy weeds] in gardens and flower beds. Be sure to add surfactant and PLEASE follow the label for gardens. Over The Top Grass Killer

Thanks for the suggestions everyone. I plan to get after it as soon as it warms up some.

If you can get the grass in the middle killed out then you can stay after the edges with a tiller or put a barrier about 6" deep. Roundup on the edge keeps it under control, just watch spraying around tree root zones. I killed 3 of my maples just spraying light.

I don't spray where I grow my food.

I ordered my seed a week or so after the first of the year. I still hadn't got it yet so I emailed the company. No reply but 3 days later I got a box in from them. I opened it up only to find a bunch of stuff I sure didn't order. Now I've emailed them two more times telling them they mailed someone else's order. No reply.

Not that I really need my seeds right now but.

Just finished planting the mater seeds and cutting up the taters.