The solution was surprisingly simple. When I wanted to stop the internal music, I focused on ambient noise. The leaves rustling in the trees. Passing cars: their tires on the pavement, brakes, engine, the exhaust note. There are quite a few things to notice. While focusing, the music stopped.
At first it took great deliberate effort to quiet the music in my head. But eventually it just went away, within a matter of weeks. I no longer need to exert effort, I have conscious control over whether I want to replay a song in my head, or just have silence.
My meditation teacher Gil Fronsdal thought of it. He's a genius.
What I prefer over TV for killing the brain noise before sleep is, again, music.
Music is the best.
I can say that forcing silence upon myself resulted in a "mental withdrawal", if you will. It wasn't very pleasant, the music gets louder and louder and quite unbearable at times. That said, I did indeed see some effects at the end, in a form of periods of silence in my mind(which was kind of spectacular for me; there's some music in the back of my head at all times). My opinion is that even longer period of non-listening would yield even bigger results.
I really recommend the experience(the deprivation, I mean; the Vipassana part is also cool, but kind of orthogonal). Even though it's very demanding, you can really put things into perspective and learn a lot about how your body reacts to things. It also gives you a completely different outlook on stuff like solitary confinement.
I don't mean to sound like I'm complaining. I love music and it's been a huge part of my life since I can remember (and I'm old).
But from my experience, I don't buy your theory. I think I'm just wired different than people that seek out quiet places.
Just stop when the brain starts picking up from there: "My stomach feels empty (BECAUSE YOU HAVEN'T EATEN AND WHENEVER YOU DO YOU EAT TRASH)" you just stop the thought on the BE and focus on the next inner or outer thing or on the next number of the count. When you can't stop the thought on time, just ignore it and move on.
At first is hard, especially with a noisy brain, but it gets easier and easier.
Similarly, I watch TV at night to dull the inner monologue in my head so I can fall asleep. If I don't my stupid mind fixates on the most negative aspects of my life (even when things are going well) and I stay awake for hours feeling horrible. TV, music, and reading can distract me and let me fall asleep peacefully.