Putting Tradescantia to use (and killing it first): how?

Hello! We are working on a minimum-effort agroecological garden around our house in Mexico: elevation 2200 m, soil clay plus building rubble, north-facing (good since climate change is heating up this place like crazy), no rain for 6 months then daily deluges in summer.
We could really use more compost but we have a bottleneck in brown matter: we don't have a lot of garden offcuts to mix in with the kitchen waste. However, the whole place is getting run over by a trailing tradescantia. I need to prune it aggressively or it grows over everything, but then I have a dilemma: how to kill this stuff in order to use it? Piled up in the heat and dry it keeps fresh and green. In a compost pile it starts growing happily with extra nutrients. In a sealed bucket, submerged in water, it seems to turn aquatic. I've got six square m of it under cardboard and thick black plastic to see if it'll die of the lack of light; it's been two months and I don't dare lift an edge thinking the five seconds of UV light will set it off again. I guess I could put it in a blender and make tradescantia sludge but, did I mention minimum effort?

How are people dealing with tradscantia? Oh, ours isn't the picturesque purple striped stuff, just bog-standard green.

More about our garden sitch in case anyone's interested or has tips: Our front garden is steep terraces held back by gabion cages. We're letting lots of "weed" trees grow temporarily to give shade and organic matter to the Japanese guava, magnolia and peaches that we want to nurture longterm. Rosemary, agaves and lavender grow bravely (and the tradescantia), everything else including nopales struggles. In winter/the dry season we irrigate with the dishwashing water.

Hola,
do you have some rabbits or cavies (cuy) to use the Tradescantia as feed? The droppings won't grow, and you can use them as fertilizer.

Does your Tradescantia bloom?  If so that might be my favorite plant aka spiderwort.

I know this doesn't help your problem.

Try picking up the inner most cardboard so you can move it to the otter edges if it looks smothered.  Keep an eye to make sure it doesn't come back to like.

Have you tried putting clear plastic over it and letting it bake in the sun?  I have killed plants that way.   Kind of like a greenhouse that gets way too hot and everything dies.  
My other favorite way to kill plants is to put a paddock around the area and put animals in there.  They might not want to eat this plant but they will trample and disturb the soil so much that the plant will not be able to grow and then you can re-seed the area with what you want to have there instead.  I would also try using the prunings you have as bedding for animals.  After they have crushed and pooped on it, the plant material may be suitable for the compost heap or incorporated in a hugelkulture bed.

Tradescantia zebrina is one of my infallible houseplants (along with sweet potato). I was given it by someone who had kept them in a jar of water for months. I have left cuttings for weeks without any water and they are still able to root after all of that.

With extremophiles like that oftentimes the answer seems to be non-disturbance. Plants like that thrive on disturbance—they take over, they hold their place, they outcompete other young plants.

Whenever I see these sorts of plants being outshaded (such as chickweed, moneywort, and ground ivy in my climate) it is because of a lack of disturbance, and allowing other plants to establish and grow over them.

Sometimes the situation causing creeping weeds to predominate is because of poor soil conditions such as those that you have, like clay and rubble. Soils like that take a longer time to deepen but it can be helped by mulch, compost, trees, and so on.

Buenos dias Emilia. I feel your pain. Tradescantia is one of the worst weeds we have around here as well. I'm part of a volunteer group that is gradually removing it (by hand) from one of the only places in this country that a rare fern grows. I also have trouble with ongoing incursions from some of the neighbouring properties and it smothers everything if I don't get rid of it quickly. When I pull small amounts I feed them to my chickens and they destroy every last fragment. For larger amounts I put them in a barrel and submerge in water for at least six months.

Since you have a long dry season in the tropics, can you make a drying rack out of branches and spread the weeds out in the sun and off the ground?

Phil Stevens wrote: For larger amounts I put them in a barrel and submerge in water for at least six months.

Phew, seems like particularly nasty stuff. I suggested the "rot barrel" method in Emilia's compost thread as a "compost tea" nitrogen source.

As a fast option, I doubt anything survives being boiled in steel barrel -- using the waste heat from making char, for example.

Permies delivers... the way you (we!) all take time to think about other peoples' problems and post solutions in complete sentences just warms the heart. Special thanks to Phil Stevens who cross-referenced my compost query!
Interesting point about tradescantia thriving on being disturbed. It's a great pioneer plant, brilliant ground cover, it just covers everything else as well.
It does flower so I guess it is spiderplant, maybe I can make friends with it too (while maintaining limits!).
I feed my snails to the neighbour's chickens, haven't tried tradescantia... in case they miss out a piece it'll engulf their garden too... better not.
Looks like I'll be spending more time in the garden. Instead of boiling tradescantia cuttings (ripped-up fistfuls in reality) I'll try smashing them into a black plastic barrel and leaving them in the sun. I'll get more coffee chaff from our friend with the coffee roastery, maybe grounds as well, for the compost. Give the most fibrous compost a second go in the anaerobic barrel. Make a new potting mix from what we have to hand: compost, clay and sand, not brilliant but that's what we have in terms of "soil" and if you buy it in sacks off other people it turns up full of pine needles anyway and the sacks decompose into really pesky microplastics.
I don't mind pootling around the garden, but hauling large amounts of matter is a problem: I mostly cycle, usually with the four-year-old in the bike seat and keeping an eye on the dog so she doesn't leap in front of traffic. Hence carting coffee grounds, chaff, manure, leaf litter etc is an issue.