Is it permissible to intentionally bring the sound of the Quran or lectures into the bathroom (such as by entering with a recorder) to make use of the showering time, knowing that today's bathrooms include both areas of impurity and cleanliness?

The words of Allah and His Messenger should be kept pure from defiled places like the bathroom, regardless of whether there is impurity in it or not. There is no need to bring the recorder into the bathroom; rather, it can be placed outside and listened to. The listener inside the bathroom might become preoccupied and unable to reflect, thereby missing the intended benefit.