Row crops were grown before herbicides came into common usage. I think it was called cultivating between the rows, or plowing up the weeds a time or two. Shouldn’t be too time consuming with the multi-row cultivators used on large tractors.
We do Minimum Till but we still cultivate, when the plants are small you can usually get everything but the top 4 inches of the bed clean but as the plants get too big you can’t cultivate without harming them and for us that is about the time the monsoons hit.