I would suspect some sort of on board interference which is affecting the IF stages of your nav receivers. These are simple AM type receivers, largely designed before modern EMC requirements.
The IF stages work at a constant frequency, independent of the frequency you are tuned to. Hence it will likely affect wherever you are and whatever you have tuned.
As you get closer to the ground station the receiver will adjust its gain taking account of the stronger signal, which may give an interfering signal more influence, hence more oscillation as you get closer. ILS circuitry is normally more sensitive given the greater accuracy required.
Test the system on the ground with an avionics test set..
How do the idents sound? Distorted in anyway?
Switch alternator off in flight and observe and change in the behavior.
Switch off any accessories, transponder, un needed electronics etc one at a time and all together, look for changes.