Grey Ghost -

Sounds like you have what you want in mind -

Overseeding may work - but to really have a chance what you should do is mow it - wait 2 weeks - then spray a ROUNDUP type product to kill all vegitation. Then overseed with an annual seed like Rye, wheat etc.

Sorghum, and corn really need to be covered to come up worth a darn. You might be able to mix some in - but for the most part - unless you can disk or drill it in - you are only feeding mice. Switchgrass should come OK - Other tall grasses are a possibility - but even with grasses - is important to expose some soil after burning off with roundup.