The Administrative Procedure Act of 1942 is an act of Congress. So I am confused what you mean by the Administrative State. It is not a real entity, correct? If any CFR or statute is not tied to law passed by Congress, or is outside the authority of the organization being created, it is unconstitutional on its face; but that doesn't mean the system of governance is unconstitutional. If organizations cannot regulate themselves, then lets go back to tribal and clan law.
Would you say the Marine Corps overstepped its bounds in creating and performing its annual "Toys for Tots" program because it doesn't have anything to do with Title 10? How about providing a color guard for a baseball game? I would argue they are recruiting tools in their best interest, but are not specified.
Getting back to NSA, the Department of Defense ultimately created it. Nothing is created ex-nihilo. Are you suggesting the President as Commander in Chief didn't have the authority to compartment and add additional resources to a military capability that already existed, with Congressional funding? DoD's mission didn't change from the Department of War. There is nothing in the Constitution that says SIGINT must be created and funded. Nor does tactical nukes for that matter.
If that is the case, then it is clear everyone didn't know what the Constitution meant. And if everyone aside from one person (you) do not understand it, then we are done as a nation. So enjoy the ride all the way to its dismemberment and let's hope for a future government that will properly address anyone in government that proposes something unconstitutional, to be led outside and shot in the public square.
“the entities by which are created and funded by Congress have to be able to create regulations by which they are governed”
Of course, but it is how the DEPARTMENT ITSELF is run, NOT national regulations and laws which is why the Administrative State is unconstitutional.
If you still want to deny the existence of the Administrative State, read this
http://thf_media.s3.amazonaws.com/2012/pdf/sr116.pdf
or this
or even this