Why Fair Use May Work
This recent case demonstrates why fair use claims may succeed ... and goes further than the activities in your question. In this case, an actual snippet of the song (an alleged infringement of the song copyright and the sound recording copyright) was used without permission of the Lennon estate. Of course, past performance is no indication of future results and the fair use argument will be weaker, the more of the song that is used. One or two lines is probably okay but use of a complete verse and chorus, or repetitious use of a song's lyrical hook, or a narrative built around the song lyrics (for example, a mystery based on Yellow Submarine) are less likely to succeed. The outcome will also be affected by the context in which the lyric is placed and most importantly, the transformative nature of the use.
Singing a Different Tune
As for singing a different melody, it's not clear how that limits the producer's liability. It might even make matters worse and tick off the copyright owner, unhappy to see the work mangled and unwilling to permit creation of a derivative work. Also, we have not addressed issues that might arise when there's a written agreement permitting the lyrics in the print book but not addressing the use on audio.
Hey ... We've Produced a Few Audiobooks, too
The Dear Rich staff takes special interest in audiobooks. (Warning! Tireless self-promotion coming up!) Besides Nolo's podcast series we've produced some exciting audiobooks on legal and non-legal subjects, and we host an informative Elmore Leonard audiobook podcast series. BTW, is anybody interested in acquiring the world's most extensive Elmore Leonard audiobook collection (described in this article)? We love talking about audiobooks. Hey why don't we make this Audiobook Week at the Dear Rich Blog? DONE!