Sorry, have not been around a few days, the fields and that 'work' thing keep calling.
Tractors between rows is a little overuse on space, but if have it why not use it.
I prefer weedblocker and sand or gravel or mix between beds with enough room to stretch out while sitting down and weeding, or staying hydrated or just admiring. The grass tends to put out rhisomes and invade the beds.
Weeds and corn, BBBAAAADDD combination. I am currently experimenting with alfalfa between the corn and close planting. Corn devours nitrogen, alfalfa puts it in. Use the alfalfa to feed the chickens when gets in the way. I think pigweed is an annual, so HAVE to get every seed that drops or even better get it before it seeds up. Ran into this issue with some compost that did not cure ehough, what a mess but cleared up pretty fast.
Vote for beds instead of 'conventional' row cropping. Can plant a lot more intensely and manage more intensily for pests. Have enough seat time (if that is possible) and like the quiet time as well.