It might be more realistic just to have the CV less sinkable....now wait a second...don't throw that!
You can damage the CV to the point that it cannot conduct air ops. After X amount of time, its repaired and comes back. If it gets hit with another X amount of ordinance in X amount of time, it sinks.
Otherwise, I like the LST idea. Sink it, no troops. Still have the problem of pork and augers, though.