Love the paddock idea, here is a slight variation of it, and I realize not everyone can do it.
My garden is 88' x 96'. Dead center in it is my garden shed/chicken coop. The perimeter is completely fenced 4' high.
I have 2 50' rolls of 2x4 farm fence that I stretch from the coop to the perimeter and rotate every 3 to 5 weeks depending on the crop.
Here's how I work it. After the second harvest, I will stretch the fences and make a paddock. The chickens will eat the late vegtables, bugs, and foilage. All while fertilizing and helping to break down the plant growth. Remember 50% green (foliage) + 50% brown (manure) = BEST COMPOST.
After the paddock is almost completely cleared I just move the fences to a freshly harvested area. Did I mention I live in Florida where we have a longer growing period?
I do have a 2' wide section of fencing buried at the perimeter of the coop to keep out predators, and I do have to shut the coop door at night. It works for me, hope it'll help you too.