I think your idea of burning is good. It will remove thatch, increase soil pH, return nutrients to the soil, and add stable carbon to the soil. Then, when the field starts to grow again, stake off about a quarter acre and nuke it. Disc lightly, and plant a diverse mix of annuals and perennials, including a lot of native wildflowers.
Within that half acre, plant a bunch of diverse shrubs. Plums, sumac, hazelnut, dogwoods, and viburnums should be helpful. These will grow into thickets that will shelter and feed the quail. They also provide habitat for a lot of bugs, which should be beneficial.
In my search for giant ragweed seeds, I came across several websites that recommend it as an ideal plant for quail. It grows tall, leafy on top, but sparse and stemmy underneath. The seeds are extremely high in protein and perfect for quail. If you're not allergic to ragweed, and you can find the seeds, nuke another quarter acre and plant a pure stand of giant ragweed.
You can also plant some spruce and pines for the little birds to hide under. Maybe cedars too.
Do you have issues with the little bluestem lodging? If so, you might want to slowly break up the monoculture by spot spraying here and there.
I'm a big fan of diversity, so I think altering the habitat with a focus on quail but with a secondary thought to other species will have a synergistic effect on the entire ecosystem and further increase the quality of the habitat for everything that lives there.