I followed the 1968 race quite closely. At the time, the notion of following the Constitution like it was black-letter law was at an all-time low (dissent from the "living constitution theory" was almost unknown). I was taught in high school that NBC = born here (pure jus soli), but Romney never got enough traction for THAT (as opposed to other issues) to become a factor in the outcome. He made his national name as an early "civil rights" supporter, the 1967 Detroit riots devalued that "achievement". By the spring of 1968, after his claim that his support for Vietnam was because he had been "brainwashed", he was out of the picture and a court challenge was never even considered.
By the way, I don't see any court getting involved in this in the until an event prescribed by the Constitution such as the electoral college meeting in December happens. The Constitution does not recognize "running for president", "being nominated", "presidential elections" as anything other than optional activities, and so any state's designation of a person as "eligible" or "ineligible" falls purely under the plenary power of its Legislature to appoint the state's electors.
I've been working out a couple of other comments, rebuttals to previous replies I have received, which I do hope are reasonable enough.
Since you do appear to me to know what you're talking about enough to provide possibly relevant feedback, look again to this thread if you'd care to comment, or correct me if I'm far enough wrong to merit it.