I've always felt news organisations should be legally required to be non-for-profit and wages capped at some sensible multiple of the national average wage (e.g 6x)
If the belief is that the press (news) should be free and unencumbered to report the truth, and accepting all solutions are imperfect, then I think its a case of removing the worst influences in alignment with that goal.
Media conglomerates and billionaires usually have competing interests due to their diverse interests and influence. So my suggestion is not to remove them or exclude them from news but to limit the number of levers they can pull within news.
I accept that my thoughts are imperfect and flawed also, so offer them for discussion and nothing else.
You're casting a pretty wide net there. I've always felt news organizations should be legally required to recruit from my exact microdemographic and only from registered members of the party I most recently voted for, with wages indexed to between 99% to 101% of my current income.