An electric starter system for a powertrain or other system having an engine includes a solenoid device coupled to a pinion gear, a brushless starter motor, and a controller. The starter motor has actual machine speed, and is connectable to the flywheel via the pinion gear during a change-of-mind event when a commanded engine auto-stop sequence is interrupted before completion. When engine speed exceeds a threshold speed and is less than a calibrated starting speed, the controller executes a method in which closed-loop speed control of the starter motor is enabled using the engine speed as a reference value until an effective machine speed is within a permissible speed delta of engine speed. The controller causes the solenoid device to translate the pinion gear into engagement with the flywheel and starter motor, disables closed-loop speed control, and commands the starter motor to start the engine.