I say they don’t have ANY at all. The whole purpose of the convention clause is to bypass a future Congress that is out of control, such as we now have. The Founders were not stupid.......
That's your opinion, and opinions are like -- ahem! -- rectums in that everybody has one. Congress believes it has a role, the Supreme Court may believe Congress has a role, and the ruling class certainly believes that Congress has a role.
Before you work yourself into a lather, print off and read those reference documents I provided. You'll see just how many gray areas there are in the amendatory process, and how your assumptions may not be valid.