Do you get other cabin noises like announcements and clicks?

I can tell you that, for me, the chimes reliably go away sometime after takeoff.  I don't think it is a huge stretch to imagine a situation where they would go away a lot sooner or never work at all.  (And I have still never heard an altitude chime.)

If every other sound works, then it might just be one of those things.  I am back to the engine sound in spot with engine off problem I thought I had fixed.  Intractable minor sound issues might just be one of those things for you, unfortunately.  Once I started using FS Passengers it ceased bothering me since I can turn the seat belts on and something happens (in FS Pax).  

Good luck with your ding dong.