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.
That is the part I think they would rely on in their attempt to set the rules for an article 5 convention. Successfully? Maybe not. But that's one of the things they will use to justify them running the convention.
Together, the counter argument is strong that an Article V convention of the states is "owned" by the states.
But you're right that the federal government will try to control it.
I will repeat this following passage from Federalist 46 from my above post, it speaks to this very issue.
But what would be the contest in the case we are supposing? Who would be the parties? A few representatives of the people would be opposed to the people themselves; or rather one set of representatives would be contending against thirteen sets of representatives, with the whole body of their common constituents on the side of the latter.
Like I said before, bring it on. Let's see a beltway elite Congress go to war with the states over this. Isn't that the reason why this part of Article V was included in the first place?
Let's let it play out and see who falls on which side. The next election after such a fight would be very interesting, assuming we will be allowed to hold one.
-PJ