I followed a train of thought recently that's somewhat related to this. It appears to me the one branch of government that has stood up reasonably well recently is the court system. Courts require a standard of evidence, and while it's clear that justices will try to interpret things as favorable to their partisan beliefs, for the most part they are not willing to simply accept alternate realities. Some people were worried that Trump's lawsuits would find friendly judges despite the lack of evidence, and that overwhelmingly didn't happen.
So that got me wondering, ironically given your listing of lawyers as one of the named bad-faith groups, could government be made to act more like the legal system, or could the legal system be incorporated more into government. One specific idea I was considering was whether you could have the option of a defamation-style judicial review of statements of fact made by elected officials. Obviously you wouldn't litigate every statement, but what if there were some sort of challenge process - perhaps with a fee to bring a challenge, and/or consequences for spurious challenges, so they wouldn't become overwhelming - by which the opposition could challenge any public statement of fact by an elected official? Critically this challenge would be brought in a court of law, with all of the professional standards and requirements that entails. (As opposed to being litigated by politicians, like an impeachment proceeding.) It wouldn't be a criminal proceeding, and there wouldn't be criminal consequences. Probably the result would simply be made public, and maybe the losing side would need to pay the costs of the winning side. Of course they would also have had the opportunity to retract and correct the untrue statement at the outset.
As things stand, the president and his supporters are able to say whatever BS they want publicly, then they go to court with these lawsuits, and they say different things, because there are actual consequences there. Perhaps if there were consequences for any knowing lie by an elected official, you'd see fewer of them? The idea wouldn't be to use this for everything, just for clear, baseless statements of fact with reprocussions. And it's not like truth is unknowable; we already have this kind of litigation around defamation, and it largely works.
Anyway, not like I see anything like this happening, but if I were designing a system of government it's something I'd want to consider. (I suppose there's also the chance of it backfiring, simply politicizing the judiciary by involving it more in politics. But again, the responses to the election lawsuits give me some hope there.)
