OK, here is what I would suggest.
Section off your poultry pasture area into at least 4 or 5 zones. Say 10' x 20'. Confine them to one zone only until they peck it to death and turn the green, green grass brown and hopefully kill it. While they are doing that, let the other zones grow. When the first one is dead, move them over to fresh ground. It will be taller grass and full of bugs weeds, etc. Turn them loose on it. Then take the dead zone and plant something green on it.
Today that might be a solid seeding of sweet peas. While they are mowing down another zone, the dead zone recovers with something green. Keep moving on down the line, killing, planting and replacing.
By the end of the summer, you should have all zones growing something fast and furious. Perhaps a patch of sunflowers? Towards mid summer, you can switch to more cold tolerant stuff like mixes of oats, rye, wheat and winter peas. Perhaps forage turnips or tillage radishes?
For now I'd avoid slow growing perennials like alfalfa, clover and timothy in favor of fast growing annuals. You might convert one or two zones eventually, but safe to assume with a small area like you have, they will destroy it PDQ.
But do manage it as a rotation of several small zones vs. one large one.
