Um, the point of litigating is not to change precedent. It is to provide a remedy for injury (or, in limited circumstances, a declaration of rights or duties).
Thus far, you have suggested two almost perfectly frivolous lawsuits.
A rudimentary problem (besides inapplicability of the Lanham Act, and the brick wall of the business judgment rule), is reliance. Reliance in a fraud case against the NYT would be impossible to prove if your allegation is that the NYT cannot be believed in the first instance because of an inherent bias in its reporting. Just what are you, as a litigant, going to offer up as conduct or actions taken by you in reasonable reliance on what you claim to be an inherently unreliable newspaper.
And then of course, there are damages. The inventive and far-fetched damage scenario in your Fordham article notwithstanding, your monetary injury would be, what, the buck you paid for the paper you don't trust to begin with?
I understand enthusiasm when in law school, but temper it when you get out, or you'll be facing some highly irritated judges with the power to impose some pretty serious sanctions.
By that reasoning, almost every lawsuit filed by the ACLU is "frivolous."