Our Shi-Tzu would sometimes get those ^*!&^$# seeds in her tail and ears when we camped at the lake.

A stitch in time saves nine so the best time to control it is when it first appears with a garden hoe. Sounds like yours already has a good toehold so longest journey start with first step. Being an annual the best approach is pre-emerge (once in Fall and again in Spring in Texas). Corn Glutton as organic and herbicides that are mostly restricted to licensed applicators. Hand control can be likened to Python control in the Everglades ,it requires lots of labor to track and kill a female but each kill prevents dozens offspring in following year, hundreds over her life. Not very incouraging I know but maybe my little pep talk can make up for it. Having grown up on a farm when weeds were controlled with hoes, 1k sq ft of garden bed looks like child's play compared to stareing at 30 arcres (only one of a dozen fields on our farm) of crop overgrown in Johnson,Crab and other grass. Unless you own 3 or 4 already, keep your eyes open at garage sales for hoes where blade and sleeve for wood handle is a singe piece. That's important ,one piece head. If it doen't already have a handle put a Hickory handle in it. This hoe will sharpen and hold an edge 5x or longer than what you can buy at big box. For a quility one piece hoe check the farm Co-Op or feed & seed. Ace can order them if they don't have them in store. If the hoe is so great,why would you need more than one? (A) Because after realizing how well it works, you accidently run over it with the tractor and break the handle you won't cry as hard if there's another ready to go. (B) I have 4 stashed at strategic spots so that I can reach it and spend 10-15 minutes or even dig out a single sprout of Johnson grass without trudging back the shed to retrieve a hoe. I often carry a hoe for no particular purpose as I stroll checking on plants or just enjoying the garden. As I see weeds I can take care of them without breaking a sweat.

This might be more to your liking. When I was taking the grandkids fishing I used a homemade trail cutter to clear paths and sitting spots. I removed front of deck on a belt driven,high wheel push mower, shortened and balanced the 22" blade to 14". The lessened cintrifical force caused by 4" missing blade on each end took some uump out of it so I bolted an old 10" steel wheel with solid tire to belt pully to bolster force. That ol bugger amazed me by chewing up finger size saplings and vines. If you have enough work to justify building it, something like that would clear plants beneath trees in your wild area. I'd think cutting.mowing chopping just after they flower would be effective in interrupting reseeding.

The stuff pulls up easily, so a metal rake can clear large areas pretty quickly. Makes for large quantities of good compost mulch! Need to pull it out by the roots. If you just chop it off, it'll keep growing.