This may be ASB, but what about Doctor Gonzo himself? Hunter S. Thompson, Vice President of the United States?
He had experience of running for office, you don't get much more covering the campaign from the inside than that, he had some talent as a political pundit, the Eagleton Affair showed that the party establishment were happy to see McGovern fail and trying to reconcile with them was a mistake.
All Out for Freak Power...why not? Couldn't have turned out worse for him than OTL.
Now, much of that is frivolous- although what a timeline it would make- but I am serious about the basic point; much like Trump today, McGovern was a renegade, not approved by the party machinery. He tried to reconcile with it, for the good of the party, and failed miserably.
Remains to be seen what the Republican renegade will do, but if Eagleton turns him down, to the point where it looks as if the party is turning it's back on him, who in the radical wing of the Democrats would do? (If MLK had still been alive...)