- stock 4.3: no problems
- stock 4.4.2: audio drops (rare)
- CM 4.4.4: audio drops (rare)
- Omnirom 4.4.4: no problems
So it's something about the ROM. I could stay on 4.3 and bear with worse audio quality and battery performance until Sony fixes it, but it seems unlikely they will bother to do something, since it seems to be an isolated issue.