Schwarzenegger 2020: Equal Opportunity to Govern

[Icelander]

Assume an alternate history with only the most miniscule changes; i.e. Arnold Schwarzenegger manages to get the Equal Opportunity to Govern Amendment (or a later equivalent) passed and/or wins a legal challenge on the grounds that Section 1 of Article Two of the United States Constitution (i.e. the 'Natural-born-citizen clause') is exclusionary, discriminatory and unconstitutional, in time to campaign for the current elections.

I'm not saying that this is in any way plausible, but I'm looking for the most realistic course of action that might ensue if some mysterious force* was enabling Schwarzenegger to win legal cases everyone expected him to lose and/or successfully lobby politicians of both parties at a much higher rate than would be reasonable.

First of all, which would seem less implausible?

Functional change in law through judicial activism, probably going all the way to the Supreme Court?

Or legal change through Constitutional Amendment?

If someone could give me some guidelines on plausible timelines, here, for whichever option they favor, that would be great.

This is a mere background detail in a game set in 2018--2019, where Schwarzenegger has been much more politically active since leaving the Governor's office and the PCs are aware of some very serious efforts to change the law. If possible, I want to be able to feature in-setting news, analysis and arguments about the ongoing process, just as background colour.

So, where and how would the first law suit be filed? How would Schwarzenegger have standing, considering that he'd have to file in the lowest court many years before the election, too soon to declare as a candidate in that election. In real life, he started in 2003 and there was a short second wind of effort in 2013, which petered out almost immediately in real reality. I'm thinking that this second wind might have been the visible changepoint.

Any comments and suggestions welcome.

*Extremelly well-concealed Alien Space Bats with oddly modest goals and a preference for enacting their nefarious schemes through the path of absolute least resistance. They will change as little as possible.