After trying to figure it out myself, I found a herbicide called Ornamec. It
deals with stilt grass and is a "spray over the top" herbicide that doesn't
affect several ornamentals but it does kill the stilt grass.

See the article http://www.ppws.vt.edu/weeds/Microstegium.pdf for more details.
Ornamec is available at the John Deere Landscaping Supply in the Triangle area.
A pint costs around $25 and makes about five gallons of spray when diluted.
Not cheap but it works.