I do not raise my sprouts to the fodder state. Simply keep them close to the kitchen sink, and rinse them several times/day. They are best to be fed out before the blade of "grass" emerges. I feed mine when the sprout part is ideally less than an inch long. The day before I feed them, I set them on the window sill so they can green up.
You can put a grow frame in your run. Lay some 2 x 4's out to make a box frame, and staple some 1 x 2, or 2 x 4 welded mesh to the top of the frame. Then simply sow your grains/seeds inside the box. You don't remove the wire cover. The birds eat the emerging green growth through the wire frame. The wire stays put so the birds can't tear the plants out by the roots.