As far as I can tell, according to the Constitution, the only ‘say so’ Congress has in the Convention process is to Log or collect the ‘applications’ from the states for a convention and deciding whether 3/4 of the states legislatures or mini conventions within those states will be required to pass the amendments. Other than that, they have no say.........
Congress has already tried to regulate an Amendments Convention, and the only thing that prevented the various Dirksen-Ervin-Hatch bills from becoming law was the lack of urgency. Get 34 states to petition Congress for a general convention, and you'll see urgency bordering on panic.
Let me reiterate my own personal feelings on the matter.
But I understand that what I want is not what I may get. There is precedent to be considered, even if the precedent's relevance to an Amendments Convention consists of penumbras and emanations. We've had major points of law decided on such flimsy foundations.