Remove before they set seed. Then continue to patrol the area for "leftovers" or later sprouter-bloomers.

I doubt any weed sprouts all its seeds at once." That's a very poor strategy when you intend to conquer" an area.

Use a coarser mulch and keep it topped off.

A coarser mulch such as what? I've been putting the Cedar Grove Compost about 3" thick on the planters figuring it would smother the seeds (can't imagine they'd germinate if they're buried that deep but perhaps they still do??) and also improve the soil in the planters.

Bark, wood chips etc. Fine composty surfaces excellent for germination of shotweed and others. Also less effective at moisture retention, you want a markedly different texture from the soil beneath in order to keep moisture in.

Don't bark and wood chips rob the soil of nitrogen as the bark/chips decompose?

Not if they remain on the soil surface.

Anytime you pierce through that mulch layer & bring up soil from below the weed seeds will resurface & sprout.

Containers are different than in ground gardens, so I've not tried a wood chip mulch in them.

You might try removing the top few inches before you add transplants then fill your containers to within 1 inch with new potting mix. If planting seeds in containers you definitely want new potting soil mix.

Control weeds in the ground around the pots. If containers are planted densely & mulched with a thin layer of dried grass clippings to cover the soil surface you may have a weed free container quickly.

Like other posters have said do patrols & remove the sprouts. It regenerates from pieces, so definitely don't use a tool to chop it up.

Corrine

Re: nitrogen and bark doesn't the soil start to decompose the bark as soon as you put it down? I don't understand how it's possible to "keep it on the surface".

It will remain on the surface as long as you don't dig it into the soil.

If you plant something new after the area is mulched, you need to pull back the mulch, plant, then replace the mulch on the soil surface.