Honestly, the phrasing kind of pisses me off.
We shouldn't even be looking for that evidence. You want to make the claim? You go find that evidence. Everyone else should just assume you're a lying turdfactory until you do so.
The story should be "Republican representatives lying to manufacture a conspiracy theory to misinform voters". We do have the evidence to conclude that. Stop entertaining their bullshit. Just call them liars and charlatans, to their faces, until they start providing evidence first.
To be blunt; their strategy is the Nazi propaganda technique of the Big Lie. And their supporters are gullible and ignorant enough to fall for it. I expect the media to be fucking smarter than that.