The least worst move is to get out. If that's not an acceptable answer, then your question is basically, "how do I become an expert deck chair arranger on my sinking ship?"
I get what you say. But are you also saying it is not possible to communicate with that style management team, and not possible to educate them about the effects of lost institutional knowledge, etc?
I feel it must be possible. The question is how. How do you survive well in such an environment?
They have no love of the product. They have no love of or loyalty to customers. They have one target, to make money, and they have their system for doing it.
The only chance you have of changing them is showing them that they can make more money doing it differently. And, because they have their system that they think works, they're not likely to listen even to that.
I feel it must be possible. The question is how. How do you survive well in such an environment?