I don't really see the problem with the Regalia. Cid himself mentions immediately that it looks similar to Garlean design. It stands to reason that anyone else seeing it would also believe it to be Garlean, or at the very least, another Ironworks invention. Ironworks is pretty damn prolific in Eorzea. They've built airships, repurposed Magitek armors, are practically creating the bleeding edge of Eorzean technology, and so on. What makes any of you think they couldn't create a car? Especially when Cid is given more than enough time to make schematics of the original Regalia while he fixes it.

Like for real, it takes barely any brain power to make Regalia "immersive" in the FFXIV world.