Doesn't change the fact that the Space Force is part of the Air Force, which is part of the Armed Forces, which is part of the Department of Defense, which is a cabinet agency reporting to the President.

It doesn't matter when the other armed forces were created. The Navy and the Marine Corps pre-date the Constitution, but the Constitution subsumes them into the Executive branch.

Find the document that establishes a private "corporation" and you might have something. But otherwise, the Constitution forms a corporate body politic in the general meaning of the word. Just like cities are "incorporated" but they are not private entities. (You have to remember that private corporations exist at the behest of the government, which can unravel them whenever it wants to.)

In any case, the Constitution is self-defined as the "supreme law of the land." Nothing can supervene over it.