You can use the 3rd parameter userToken of ProjectAsync like so:
_geometryService.ProjectAsync(new List<Graphic>() { projectedGraphic }, new SpatialReference(4326), projectedGraphic);
and in the Completed event, you can retrieve graphic with attributes through the UserState:
void geometryService_ProjectCompleted(object sender, GraphicsEventArgs e)
{
Graphic projectedGraphic = e.UserState as Graphic;
// TODO: complete project completed logic here.
}