Under longstanding principles of contract law, when it comes to an Amendments Convention, the states are the Principals, the convention is the Agent, and the language of the petitions to Congress from the states constitutes the Agency Agreement. An Agent is bound by his Principal to his Agency Agreement and cannot go outside it. Responsibility flows downhill in this schema.
This is why the assertion that Congress should have called an Amendments Convention in the 1890's is not consistent with normal jurisprudence. The fact that two-thirds of the states requested a convention for a variety of subjects dating back to 1789 is irrelevant, and so is the further assertion that all Amendments Conventions are general conventions open to all subjects. The states may request a general convention, and if they do, the Agency Agreement stated in the convention call will specify a general convention. This goes back to the "interstate conventions" called under the Articles of Confederation, of which some were single subject and some were open to all subjects. But if the states request a single subject convention, that language will be extracted by Congress from the state petitions and inserted into the convention call as the Agency Agreement. The convention call's job is to name a time, place and subject matter.
The ABA Document came up with a clever suggestion to protect the states from a recalcitrant Congress. It suggested that when a state sends a petition for a convention to Congress, it names the states that have also submitted similar petitions. This is to make sure that Congress tabulates the petition in the correct column, rather than saying that a word or bit of punctuation requires tabulation in a separate column. Because Georgia has petitioned with some good comprehensive language, other states should use that language, and upon sending it to the Archivist for safekeeping and tabulation, the petition should state plainly that it should be tabulated in the same column as Georgia. This would put Congress on the spot.
In other threads, I've gone into detail about the 1967 debate in the Senate about whether Congress could find a legal way to defy the states and refuse to call an Amendments Convention once the threshold has been reached. I would refer to what happened in 1992 when the 27th Amendment, proposed by Madison in 1789, crossed the three-fourths threshold.
The Archivist, under current law, sends a memorandum to Congress when an applicable threshold is reached. Until then he is under no obligation to warn Congress that something is brewing. When Madison's Salary Grab Amendment hit 38 ratifications in 1992, the Archivist blindsided Congress with his memorandum. Congressional leadership sent a letter to the Archivist demanding that he rescind his memorandum because the older ratifications were "stale" and had to be done over. The Archivist sent a brilliant letter back to Congress quoting every applicable Supreme Court decision and tossed it right back in Congress' lap. There was brief consideration of having Congress sue the Archivist in federal court to get a decision more amenable to Congress, but because 1992 was an election year, the congressional power brokers decided that the optics of Congress openly defying the Constitution's amendatory process would make a bad electoral situation worse. Congress swallowed hard and accepted the 27th Amendment into the Constitution by the usual parliamentary method of a Joint Congressional Resolution.
The key here is "optics". While one can discuss various scenarios about Congress potentially defying the will of the states, I don't see it happening. Once the Archivist sends his memorandum to Congress, I fully expect Congress to swallow hard and generate a convention call in a Joint Congressional Resolution naming time, place and subject matter extracted from the petitions.
What I do expect Congress to do is expand the Supreme Court's 1921 Dillon decision and 1939 Coleman decision in an attempt to regulate an Amendments Convention according to the suggestions of 1973 ABA Document. As Levin has pointed out, an Amendments Convention is the property of the states, and my personal belief is that Congress has no business inserting its nose into the process other than executing its solemn constitutional duty of issuing a convention call. But there are enough gray areas in the amendatory process, eloquently defined in the ABA Document, that I would expect Congress to butt in and the federal courts to rule on it.
Well ain't that a surprise. And who, on the people's side, would have any confidence in this process, given that the courts are rife with progressive judges. Congress won't go after the lawless Obama but would go after the people and the states? Such is the stuff of revolutions.