I think I'd do something in your garden intentionally throughout the winter...maybe grow kale, beets, cold weather spinach, etc. in low tunnels and let them graze them alternately~they will keep regrowing tops if you only let them graze it lightly~called "creaming" the crop~before switching them out. Plant into wire or plastic mesh to keep them from scratching out the plants themselves . In between the rows, plant white dutch clover.
In the garden in the spring plant millet, sunflowers and field corn for a winter supplement and I'd ferment it before feeding. This will stretch your ration's total protein levels by making them available for absorption by a monogastric animal, by increasing the villi and total absorption area, and also increasing the overall health of your flock by creating an intestinal environment that is not good for parasites. Supplement this feed ration with some animal fats and calcium by finding a source for bone meal and fat trimmings.
In your runs I'd start a deep litter in one side that would mimic the forest floor so that the excess nitrogen that it is receiving will have something with which to bind...in other words, compost the whole darn thing on one side, let the grass grow in the other. This can be done by adding all your leaves, weed and grass cuttings, twigs, sawdust, pine needles, etc.
The composted side will be your "sacrifice" area, something farmers often have in the winter months to keep livestock off their pasture in order to let it grow without being damaged by overgrazing and pugging. Also can use deep litter in the coop as well, to keep their entire environment balanced and to attract those beneficial nematodes, yeasts and bugs that will prey on parasites in the coop environment. The compost in the run will keep the soils there spongy and able to absorb fluids, thus providing a way to cleanse the run of a build up of nitrogen, while the beneficial bugs and worms will be attracted to the nutrient rich soils under the compost. Let the birds keep it aerated for you but also give it times of rest. Tend it well and you will have healthier chickens and soils.
Then intentionally sow your other, grassy side with some white dutch clover, fall fescue and other perennial grasses and give these time to get established before letting the chickens in there and only let them in for a limited time until the grasses have had time to reseed themselves the first year and then just work it on a reproduction cycle and use it lightly...you always have the sacrifice area in which to turn them back into.
I would also not overstock the soils in your small area by running a larger flock...I'd keep it to a 15-18 bird minimum and you'll be glad you did. The area that you describe is too small to keep 30 birds for long without overworking the soils and encountering health issues in your flock. Think in terms of years of your livestock living on this same place and how much nitrogen it can handle, then try to do a smaller flock very well instead of a larger flock and always be desperate to provide them food and healthy environment.
In other words, when free ranging, I'd never put more than 50 birds to an acre if I wanted it to be sustainable...and even then it better have great forage opportunities with both meadow and woodland. Thirty chickens to .03 of an acre is way too much over time, even with resting the
land by placing them in a run. When wanting to be able to grow their feed on a small area, it is wise to think smaller flock, smaller needs from a smaller place. Make the proportions fit and it won't be such a struggle to keep things green on your land.
For information on fermenting the feeds you are currently feeding, thus saving money and giving your flock a health injection, you can read on this link:
http://www.backyardchickens.com/t/644300/fermenting-feed-for-meat-birds