Sounds like the grass is not doing You or the birds any good.
Around here for a while all they planted in ditches etc was Sheep Fescue, or a mixture of warm season grasses including Sheep Fescue.
Sounds like that may be what you have. Mixed with quack grasses and June Grasses. Maybe some perennial ryegrass.
If it were mine I'd go into there with a tractor tiller, stir it up good. Alfalfa and Sweet Clover. Planted with Millet or Black Oil Sunflowers. Yes You could mix in some Side Oats Grama and Little Blue Stem. The grasses don't provide much Winter cover. After the first year the Sweet Clover will grow tall and rank along with the Alfalfa will make good Winter cover and food.
You will get lots of weeds, but for the birds, that's a good thing.
I would get in a system where I would do a patch each year, then rotate about every third year.
Don't mow or spray.