hi Nicole
http://www.nps.gov/plants/alien/fact/mivi1.htm
Mechanical
Stiltgrass can be mowed in late summer (i.e., August through September) when the plants are flowering but preferably before seed is produced. This can be done using a lawn mower or "Weed Whacker" type machine or a scythe. Because stiltgrass is primarily an annual plant, cutting late in the season before the plants would die back naturally avoids the possibility of regrowth. Recent information suggests that stiltgrass plants that are cut early in the summer respond by regrowing and flowering soon after cutting, much earlier than they would normally flower. This is another reason to consider cutting in late summer to fall rather than during the early summer months.
maybe if you cut it before it goes to seed and let it lay
then plant a winter crop like rye there which will grow when tree leaves fall
the rye would grow over the winter, helping to stabilize things
and in the spring the rye might crowd out the stiltgrass before the trees shade out the rye...
I don't know if it would work but I don't see that it would hurt and wouldn't take much effort
that's my thoughts anyway
good luck