The latest Raspberry Pi firmware update does indeed resolve the audio frequency issue I was seeing. My test laserdisc image file (with a continuous sine wave as the audio) now sounds smooth with no breaks or pops.
This audio testing reminded me of another audio issue that has been reported to me in the past: when the sound initially starts playing, it does not seem to be properly buffered because it kind of stutters before it gets going. I will look into this next. My design should've prevented this from happening so I am curious why it's not working :)