An other good weed management option that is underutilized: Flame weeding. If I had a longer season, that would be my go to approach. If I tilled, I'd prep the seed beds, then let them rest till those little weeds made a good cover. Flame it, wait an other week or two, rinse and repeat. Every time you till, you are exposing a new crop of weeds. Other option would be to cover with clear plastic for a few weeks to solarize the soil. That will steam out the weeds on the surface. When planting, disturb the soil minimally.
I used the flamer when treating the cedar framework for my raised beds. Pretty efficient tool to scorch a lot of material very quickly.