Assuming for a moment that the bent tab isn't touching anything else metal other than the player...

I wonder if there is a bad/intermittent contact between the player docking connector and the car sled docking connector. You know: the part that's supposed to dock and undock, the wiggly thingy in the back. And that the bending of the tab is changing, slightly, the positioning and pressure of that contact. Sometimes it makes good contact, therefore no whine. Change the angle that the player seats into the sled, it makes poor contact, you get whine.

Have you tried simply cleaning the contacts?