That language in Article V pertains to Congress, but not to an Amendments Convention. If you read the ABA document, the authors point out that an Amendments Convention possesses enough sovereignty to decide its own rules for passing an amendment to Congress for disposal and then to the states for ratification. The Convention can choose a two-thirds threshold for reporting out an amendment, but it does not have to. I believe that even the ALEC document concurs on this.
The 2/3rds requirement is for Congress to pass an amendment, but it is also for the states to call for a convention to propose amendments. As you point out, the 2/3rds number is not for the convention to pass an amendment; that is up to the convention to decide. It is only the threshold for Congress to call the convention in the first place.
-PJ