The problem is that Natural Born Citizenship is only a factor in eligibility for the Office of President. No such case has ever come before the Court, so they have had no cause to rule on the issue. There is dicta on the "of two citizens born in the country" part of Vattel's criteria, (cited in Wong Kim Ark, but dicta even in the original case) I know of none specifically on the "in the armies" provision of Vattel.
So, it’s back to saying that children born abroad to parents serving in the military are citizens, and that citizenship is determined via statute, going all the way back to the 1795 Act. Any form of citizenship above and beyond that, cannot be shown via any relevant decision, implied by statute or even implied by the deliberate omission of a statute, as in the instance of the 1795 Act.
Vattel and Blackstone dealt with this issue similarly, but neither appear to clearly be the definitive source for any determination of Constitutional citizenship for children born under such circumstances... which is fairly close where I was before we began this discussion.
Maybe multiple sources might have been considered for such foreign births, with little available in the way of appropriate, specific guidance or precedent, creating the need for a novel solution, “de novo” I suppose would be the appropriate term? The United States was, as I understand, regarded as being the first Constitutional Republic. Pursuing such an avenue might not clarify matters at all.
Your previous comment, about the original 1790 Act being indicative of a recognition that such foreign births were not covered under the Constitution, would seem to be something to dwell upon.