Even with enough lead time, displacing as much mass as possible at just above escape velocity is the most efficient impulse transfer. For an asteroid of appreci

Even with enough lead time, displacing as much mass as possible at just above escape velocity is the most efficient impulse transfer. For an asteroid of appreciable size, your tiny thrust would have to be not-so-tiny anyway. (Plus, chances are that a large mirror stimulating the Yarkovsky effect might be more efficient at this, and without the issues that a prolonged contact with a complex spacecraft might bring.)