Maybe this requirement to have Congress actually call the convention is useful as some kind of verification step that the legislatures of 2/3rds of the states actually did apply. But unlike Hamilton, I don’t trust those politicians because they know this convention will take money and power away from them. I could see Congress doing everything they could to delay and stall until maybe some new state legislatures were elected who would oppose such a convention. I say if the legislatures of 2/3rds of the states applied and Congress stalls, have the convention anyway on the grounds that Congress (once again) is behaving unconstitutionally.
Some history is in order here.
By 1967, some 32 states had generated petitions for an Amendments Convention to reverse Reynolds v. Sims and Baker v. Carr, better known as the One Man/One Vote decisions from 1962. When the Senate discovered that we were only two states away from an Amendments Convention, all hell broke loose.
Sen. Everett Dirksen, the Illinois Republican, offered a bill to set up the operating rules for an Amendments Convention. Two Supreme Court decisions, Dillon v. Gloss in 1921, and Coleman v. Miller in 1939, gave Congress wide latitude in regulating the amendatory process, provided such regulation did not contravene the plain language of Article V. Dirksen wanted to set up the rules so that things would not get out of hand, producing an infamous runaway convention.
Two Democratic senators from Maryland, Joseph Tydings and Daniel Brewster, argued that Congress could and should ignore some of those petitions because they had been generated by state legislatures that were mal-apportioned by the rules of the Reynolds decision. Both were eventually to go to prison.
The other senator from Illinois, Chuck Percy, a Republican, argued that Congress had to ignore those petitions because an Amendments Convention would be run by the worst elements in American politics, by which Percy meant conservatives. Percy would lose his seat in 1980.
The arguments were based on the idea that Congress was a sovereign body, and no court could tell it what to do in its internal processes. But that was before the Powell decision.
Dirksen died in 1969, and his bill died with him, although it was resurrected in various forms by Sam Ervin of North Carolina and Orrin Hatch of Utah. No version was ever enacted into law.
Remember Adam Clayton Powell? He was the black minister and sleazeball congressman from Harlem who was not seated by the House. Powell sued in federal court, arguing that he had fulfilled all the rules of the state of New York to be elected a congressman, and the House had to seat him. If the House wanted to expel him, that was fine, because the Constitution requires a two-thirds vote of the House to toss him out. But the House had to seat him first.
This case went all the way to the Supreme Court, and along the way there were stern warnings from congressional barons that the Court should stay out of this for reasons of separation of powers. The Courts decision ordered the House about like a lackey, telling the House fo seat Powell, which it did. The House could have impeached the justices who made this decision, but it decided that discretion was the better part of valor. Eventually, the voters of Harlem tossed Powell out and put Charlie Rangel in, where he remains to this day.
The Powell precedent is cited by those who believe that if Congress refuses to call an Amendments Convention after being petitioned by at least two-thirds of the states, then the Supreme Court could order Congress to set a time and place for the convention. Or perhaps the Court could call a convention on its own authority. An activist Court like Earl Warrens might have taken such action, but I question whether John Roberts Court would do so. The Court might declare congressional intransigence to be a political question, and say that it is up to the voters to replace recalcitrant congressmen and senators if they really want a convention that badly.
I would recommend you go back to that boilerplate post with the links to documents and print those documents off. The ABA document, in particular, looks at all the gray areas and loopholes in the amendatory process.