Perennials vs. annuals in chicken pastures

In the last year, I've been experimenting with crops that I can grow in the chicken pasture to give the chickens extra food.  After rotating chickens to a new pasture, I've seeded bare patches with buckwheat, beans, wheat, field peas, oats, clover, ground cherries, lettuce, amaranth, sunflowers, and pearl millet, and have discovered a couple of flaws in this plan:

• Planting annuals slows down the rotation.  Our chickens get the most free food from pasture during their first week on fresh ground, but it generally takes at least a month or two after planting before I feel that crops are tall enough to allow chickens back into an empty pasture.  That tends to slow rotation down significantly, leading to overgrazed pastures like the one shown above.
  
• Chickens don't like cultivated food as much as wild food.  Over and over, I've turned chickens into pastures with mature annual crops...and the chickens have walked right past the cultivated food to eat chickweed or grass seed heads.  Clearly, I'm not as good at guessing what chickens like to eat as nature is.
• Seeds scattered on bare ground are eaten by wild birds.  Although I don't have this problem in the garden, the pastures have a small enough human presence that I have to bury seeds if I want them to come up.  Since the areas chickens scratch bare still have roots holding them together, this is tough to do without tilling.
  

On the other hand, the forest pasture (and the forest beyond the pasture) hold nearly endless appeal for the chickens due to the complexity of the environment.  Leafy areas under shrubs are great for worm-hunting, a different weed always seems to be sending up tiny fruits that the chickens relish, and there tend to be lots of flying and crawling insects in a diverse environment.

As a result, I'm changing gears and starting to plant perennials in the chicken pastures, especially trees and shrubs that will add complexity to the pastures' ecological structure.  I've discovered that it's pretty easy to keep the adult chickens out of newly planted and mulched areas by making a quick and dirty fence out of four fence posts and a length of plastic trellis (although our tweens did squeeze into one of these areas and demolished two young grapevines.)  In a year or so, I'll open up the fences and let the chickens enjoy the leafy areas beneath grapevines, timber bamboo, mulberries, and almonds.  As an advocate of permaculture and (especially) forest gardening, I should have guessed that pasture structure would be more important to chickens than pasture contents.