To interpret the Elastic Clause as noted in the OP - that it "gives Congress the power to do stuff not otherwise listed in the Constitution" - negates any need for anything else in the constitution, say nothing of the other 17 clauses in Article I Section 8.The clause id question is below. I tseems pretty clear that the framers were referring to the powers enumerated above this clause. I don't see any other way to read it.
"To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof."
If the action does not concern the "foregoing powers" or the "other powers vested by this constitution", it's obviously not allowed in this clause.
This doesn't require legal expertise. Just the ability to read.
The cited interpretation of the EC is, without question, as incorrect as incorrect can be.