Dealing with Common Quickweed

Hey there permies,

I tried searching the forums, but wasn't able to find anything relevant. If I missed something, please feel free to let me know.

Context: Weed infestation in our annual vegetable garden. Approximately 3800 ft^2.
No till

Partially under a hoophouse. Intermittently using water-permeable DeWitt landscape fabric (not my favorite idea at all, but I was desperate against the weeds).

I'm dealing with a wild infestation of common quickweed (shaggy soldeier, galinsoga quadriradiata). I suspect it came in off of a batch of donated compost years ago and it's just been spreading every since.

For the first few years that we had it, I was able to keep up on it via intensive (time-consuming) weeding - pretty much a HEAVY weeding every single week to try to keep it at bay. Since having kiddos, I've been slowly losing the fight to it. Over the past two years, pregnancy complications and a needy newborn rendered me pretty much absent in the garden and it showed in the proliferation of this horrible weed. It basically took over the garden.  

I'm trying to figure out how to decrease its presence (I'm pretty sure eradication is out of the question).

Solarization? In combination with super-duper thick mulch?

Any other brilliant ideas? I'm at my wits-end.

My Approach to annual weeds

As an annual, galinsoga quadriradiata lives a fragile early life. It pulls or rakes out with almost no effort immediately after germination. Shallow disturbance at the right moment—nothing intense, just a light pass with a rake or hoe a day or two after the first sprout—breaks most of the seedlings. With minimal soil disruption, the deeper seeds tend to stay asleep, and the surface seed bank gradually declines.

Timing feels like the real magic with annual weeds. Many of them germinate in one big flush when warmth, moisture, and day length align. If I wait to plant my vegetables until that first flush appears and I sweep it away, the follow-up flushes seem tiny in comparison. The crops rise with much less competition, and I spend far less time fighting nature. Planting much earlier than the annual weeds germinate can shade them out.

I prefer to avoid the heavy work of solarizing or smothering unless I want to reset a bed entirely. Often, simple shallow passes—done early—shift the whole dynamic. Galinsoga grows fast, yes, but it also surrenders easily when dealt with as tiny plants.

Wishing you more joy and less struggle in the garden.