Pasture reclaimation for annuals

I’ve got a 1000 sq ft paddock that was formerly my sheep’s sacrificial Winter lot. In the grazing months I grew sunflowers. The sheep are now gone (change in my availabile labor hours), so year 1 I planted pumpkins and corn in addition to the sunflowers. In year 2, the weeds outpaced my crops, and now in mid August I’ve got thick variety of weeds 5 ft high, no pumpkins or corn, and only a handful of sunflowers. I had mowed the weeds to the ground when I did my direct sowing, but it seems the weeds outcompeted the crops.

I’m familiar with cardboard and wood chips methods, but not sure how you do that with directly sowing beneath.

How do you reclaim pasture for annual crops without tilling?