An Article V convention to propose amendments is for the States. Amendment 10 grants to the states all powers not delegated to the United States.
It seems to me that the power to control an Article V conventions falls to the states via the 10th amendment, since it is a convention of the states, by the states, and for the states.
-PJ
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.