Cape weed Arctotheca prostrata

Hi Permies,
Does anyone know what a "solution" might be for this South African perennial herb that is considered invasive (problem) here in California? It is a pretty ground cover with bright yellow daisy like blooms. Kind of aggressive, doesn't live in polyculture, perse... I found a research paper that describes it as allelopathic. We have two large swaths of it on our land. It seems to do well where cows used to congregate and compact the soil.
It also seems to bounce back quickly after being driven on and otherwise mashed. I think it propagates easily from chopped up root material too. it scythes nicely but I'm hesitant about making a compost pile with it (or mulching for crop beds). Any ideas or thoughts appreciated!

here is Calflora's page on it Calflora

When I have plants that I don't want to put in regular compost for fear of them spreading, I either dry them to the point of crumbliness before composting, or else waterlog and ferment them. We use those big plastic 55-gallon barrels they ship olives, apple juice, etc. in, and I use those. If you don't mind the stink, just put them in water and rot til they fall apart. If you would prefer a less anaerobic situation, use an aquarium bubble stone, just as you would for making compost tea. Throw in some bokashi or other benign fermentation bacteria if you have it.
In situ, I don't think they can withstand cardboard mulch, if the area is small enough for that to be possible.