The perpetual union predated the Federalist papers. After the perpetual union, came the “more perfect” union under the current constitution.
A perpetual union, perfected, and the secession as practiced by the late rebellious states was of no legal effect, as determined by the Supreme Court under Texas v. White.
Also, and the libertarians tend to forget this, the Federalist Papers ARE NOT in any way shape or form codified law. They are nothing more than essays of private individuals (yes they all held government posts, but the anonymity of Federalist Papers makes them private with no official bearing) conveying their personal opinions about the nature of government and reasons why the Constitution should be adopted.
The "Perpetual Union" ceased to exist the minute the ninth State ratified the Constitution -- by doing which, by the way, all nine of the ratifying States seceded, as admitted by James Madison in The Federalist, from the Perpetual Union.
By ratifying the one, they necessarily and ineluctably seceded from the other. Illegally, no less.
You will now concede this point and this argument, right now, forever, as a basis of further discussion. Give it up. Give it to me right now.