Frankly, but only in my opinion, I think you may be over-complicating things a tad.
To say there is an inherent paradox in Chapter I, Article IV of the Westminster Confession (hereafter, WC) is simply not accurate.
In writings generally and not just in religious writings, for there to be a paradox there needs to be either a real contradiction or an apparent contradiction. What is contained in the Westminster Confession and other universally agreed upon statements of faith (e.g., The Apostles' Creed) is not a paradox but a defense of a presupposition; namely, the Bible is God's Word, and its authority derives ultimately from God.
What has been given short shrift in the WC is the role and instrumentality of the writers of Scripture, who because they were, in large part, prophets (in the Tanakh) and apostles (in the New Testament), the books which found their way into the canon of Scripture did so because they were recognized by literate Jews and Christians to be the Word of God, and not just the word of men.
Peter realized this fact when he said,
So we have the prophetic word made more sure, to which you do well to pay attention as to a lamp shining in a dark place, until the day dawns and the morning star arises in your hearts. But know this first of all, that no prophecy of Scripture is a matter of one’s own interpretation, for no prophecy was ever made by an act of human will, but men moved by the Holy Spirit spoke from God (2 Peter 1:19-21 NASB, my emphasis).
Additionally, Peter recognized the apostolic authority which resided in the apostles' teachings in general and in the words and teachings of the apostle Paul in particular because those teachings came from the Master directly and sometimes indirectly. As for the Master's deeds, the disciples and apostles were eyewitnesses (see, for example, Luke 1:2 and 2 Peter 1:16). First, the prophets and apostles in general:
This is now, beloved, the second letter I am writing to you in which I am stirring up your sincere mind by way of reminder, that you should remember the words spoken beforehand by the holy prophets and the commandment of the Lord and Savior spoken by your apostles (2 Peter 3:1-2 NASB, my emphasis),
We also have the prophetic message as something completely reliable, and you will do well to pay attention to it, as to a light shining in a dark place, until the day dawns and the morning star rises in your hearts. Above all, you must understand that no prophecy of Scripture came about by the prophet’s own interpretation of things. For prophecy never had its origin in the human will, but prophets, though human, spoke from God as they were carried along by the Holy Spirit (2 Peter 1:19-21 NIV, myemphasis).
Interestingly, Peter considered the "prophetic message" as contained in the Tanakh's Law, Prophets, and Writings to be on a par or even superior to his own eyewitness testimony! Peter, in my opinion, was not just being modest in his apparent discounting of his testimony as an eyewitness but was simply reflecting the confidence which Jews at the time had in the Tanakh.
Now, for Paul's apostleship in particular:
Therefore, beloved, since you look for these things, be diligent to be found by Him in peace, spotless and blameless, and regard the patience of our Lord as salvation; just as also our beloved brother Paul, according to the wisdom given him, wrote to you, as also in all his letters, speaking in them of these things, in which are some things hard to understand, which the untaught and unstable distort, as they do also the rest of the Scriptures, to their own destruction (2 Peter 3:14-16 NASB, my emphasis).
Peter may not have known that his two letters would one day find themselves in the canon of Scripture, but he certainly did know with full conviction and assurance that the apostle Paul's teaching had the apostolic ring of truth to it. Peter put Paul's teaching on the same level as "the rest of Scriptures." (A good question to ask at this juncture would be, "To Peter, what constituted 'the rest of Scriptures'?" but let's not complicate things any more than they need to be!)
In short, though the canon of Scripture came to fruition over the course of centuries, what constituted its various parts as being God's Word was the acknowledgment of the church universal (beginning in Jerusalem, of course) that some writings were "Scripture" simply because they originated in the apostles' teaching.
We must not forget at this point, however, that God was at work through his Holy Spirit in the early days of the church in the dual processes of the inspiration of his Word and the preservation of his Word. In a sense, what God did by first providing and preserving his Word in the Tanakh, he simply repeated by inspiring and preserving his Word in the New Testament writings.
The process by which the canon of Scripture was codified, preserved, and transmitted faithfully over the centuries, a process which included the creation of creedal statements such as the WC and The Apostles' Creed, may seem to smack of circular reasoning at best and paradox at worst, but I believe it does not. Positing a belief (and the statements which support that belief) on bedrock assumptions or presuppositions, as the writers of the WC did in Article I, Chapter IV, did not involve a statement that is self-contradictory or logically untenable, which is at the heart of a true paradox. Rather, the positing of that belief was based on a valid deduction from acceptable premises.
By and large, the writers of Scripture claimed either to be speaking and writing on God's behest ("Thus saith the LORD," the original prophets said repeatedly) or they claimed to be repeating the words, teachings, and deeds of Jesus faithfully and with the corroboration of all the apostles. Once the apostles, disciples, and other eyewitnesses of the life and teachings of Jesus had died, God was obviously at work in preserving his church by preserving his Word and the faithful transmission of it through each successive generation of Christians.
False teachers arose in the first century AD within years of Christ's ascension, but faithful teachers, preachers, translators, copyists, church councils (and much later, printers!) then made sure that subsequent generations of Christians would have a faithfully transmitted copy of God's precious and eternal Word. This process does not involve paradox or circular reasoning; it's just the way
God decided to reveal his Word to the world.