An engine control system for a vehicle includes a shutdown control module that generates a command to shut down an engine of the vehicle when at least one of: a driver requests the shutdown of the engine via an ignition system; and when one or more predetermined conditions are satisfied for shutting down the engine without the driver requesting shutdown of the engine via the ignition system. A valve control module, when the command to shut down the engine is generated, advances an exhaust camshaft phaser based on a predetermined exhaust park position. When the exhaust camshaft phaser is in the predetermined exhaust park position, an exhaust valve of a cylinder is fully closed during an exhaust stroke of the cylinder before a piston of the cylinder reaches a topmost position for a next intake stroke of the cylinder.