Sorrel: is there any way to stop it strangling my garden?

How do other Permies deal with sorrel in the garden?

It doesn’t seem to be much of an issue in our house garden, but in our other garden it has been taking over in some beds and preventing things from growing. Our old way of preparing beds in this garden was to thoroughly broadfork over them and remove roots, I delegated a lot of this work to other people last season and I’m not sure how thoroughly it was done. We have massive sorrel problems now.

The house garden is chicken tractored, and the garden with the sorrel problem isn’t, so I am wondering if running chickens over the garden with a chickshaw/portable netting approach in sections would get rid of the sorrel? Has anyone tried this and succeeded?

Has anyone tried clearing sorrel with pigs?

Another approach might be to figure out which plants will quickly outgrow and shade out the sorrel, and which plants aren’t bothered by the sorrel, and to concentrate on growing a lot of these - has anyone used this approach? Which crops do you find will handle the weed competition?

And another idea might be to plant lots of rye as a green manure and hope that the tall growing habit and allopathic effect on it might help - has anyone tried this?

I am also working on improving the soil and bringing pH up from ~pH 5.3 by adding lime and other minerals, as well as wood ash and organic matter, so hopefully this will help in the long run.

I have no ideas, but I am interested in what you come up with.
When I hear sorrel I think food, but I'm sure there are multiple kinds, and too much if anything can be an issue (Himalayan blackberry for example)

I only get it in sour, well drained, poor quality soil.  Once I get some organic matter and woodash in the soil, it's gone in a year or two. And replaced with far more vigorous weeds.

I try to keep a patch on the go as it's the most delicious of the wild salad greens.

I'm dealing with a few sorrels myself. The small type which covers and the big ones that never die.
Repeatedly cutting them has taken care of the most persistent ones in the main beds, digging them out with a trench shovel and repeatedly digging out the smaller offshoots with a hori hori knife i carry in a builders pouch has done that.
But in the wetter spots the big ones seem eternal. I keep cutting them down with a zeiss. Busy growing Russian comfrey over them now. Dumping straw on them all the time helps a bit too.
But when i turn my back they're back again. Can't say that i really, really care. Usually i go on a rampage against a plant because i can't control them, in fact i am the problem, i've realised over the years going on campaigns against native plants. I tried to kill all yarrows until i realized it cures my trees, my wild violets out of fear they'd take over... Madman style. I try to consider them free mulch now, and those roots might have a good function, leaving plugs rotting down in the soil, opening it up.
It sure looks messy though, but visitors i can't take them seriously any more since my neighbor lady who never grew anything more then the rose she spends a hundered bucks a year on ciding it said all i grow is weeds and her husband visiting later saying i do permaculture all wrong, i have to mix everything up much more.
But my project is with the farmer and keeps expanding and expanding, so i'd better not care too much, when it would be limited i'd care probably.
Trying wintercereals rye has helped a bit too. Parsnips have the same function a bit and are edible and self seeding where i am, daikon, black radishes, make these crazy roots, could have the same function...
Good luck!

Once I decide something is delicious, I never have too much of it. I do the work of the chickens. :)

ETA: the kind of sorrel I mostly eat and tries to take over my garden is in this post: https://permies.com/wiki/75/111863/pep-foraging/Prepare-dish-PEP-BB-foraging#1855098

Do you have chickens?

Sorrel is edible - and if not to your taste then the chickens will eat it. When I have time to work on my garden I typically aim to weed a good basket worth of chicken snacks at a time. It adds up pretty quickly if you can do it consistently.

Our big pests are bindweed and creeping buttercup.  If I chuck a basket into the chickens they will generally strip every leaf within 24 hours, which saves me on food bills. I'm sure they would do the same for your sorrel.

I like to tackle one area thoroughly, rather than spread myself out too far. It's particularly effective in areas where you can mulch heavily with eg woodchips, as each time you come back to do more weeding they will be both more sparse and less strongly rooted in the chips.

Now, if only I didn't work a 70+ hour per week job...