No, you're making it about the government, because you're talking about the enforcement of a "should" action, and it's the government tasked with the enforcement. As such, there's absolutely zero way around the fact that you'll be instructing the government to be the arbiter of what the actual truth is in order to enforce your standards. If you don't want to go down the rabbit hole, Alice, start by not jumping directly into it with both feet.
Further, these media don't "seek" First Amendment protections. They have them, guaranteed by the Amendment in question, which does not issue caveats nor carve-outs in it's language. You're asking for a new interpretation of the Document which would create a new type of unprotected speech, and the speech you're looking to exempt from Constitutional protection is political speech.
It's absolutely beyond me how you don't view these things as absurdly problematic.