The convention process is created by Article V; it is not a component of any of the three branches of government created by the first three articles. The convention derives its power from a separate and independent grant of authority in the constitution itself. It cannot be made subservient to any branch of the government. Further, the sole purpose of the convention is to propose changes in the pre-existing system of government. This renders the convention distinct from, if not superior to, the three branches of government.
Delegates will serve their states. They will have no attachment to any statutory authority under the US.
According to Madison, the Whole People created the Constitution and the Union by use of their separate political societies -- the states -- who were the agents of the Whole People. This sovereignty supersedes that of Congress. Why? Because the Constitution, which is representative of the Whole People via their states, created Congress. Congress did not create the Constitution.
In this case, the sovereignty of the Whole People, via their states, supersedes the sovereignty of Congress.