But you still have to rely on the Church's judgement as to which books are Scripture. What ever criterion, other than the Church's judgement, you purport to bring forward ('undoubted apostolic authorship' is the usual one you sola scriptura types usually propose), you have no criterion for verifying that the canon of the New Testament and no other books satisfy it other than relying on the ancient Church's judgment and the long tradition of the Church.
If you trust the Church to have judged rightly which books are Scripture, why do you distrust the Church's judgement on other matters?
Again, what evidence can you set forth that the Holy Spirit led the Church correctly to fix the canon of Scripture at the Council of Carthage and the Fourth and Sixth Ecumenical Councils that ratified that local decision, the former implicitly in the phrase 'ancient canons', the later explicitly, but that the Fathers went astray at the Fifth Ecumenical Council?
What evidence do you have that you exist? You are asking the impossible. You are asking me a question like "prove to me that God exists and is exactly as He appears in the Bible. I can give you reasons I believe, but no proof that will satisfy you.
Nevertheless, I'll take a crack at it. I believe what I believe for the same reasons you believe what you believe. I accept by faith that the Holy Spirit led the early church concerning what was canonical. My faith is bolstered when I actually study the books and see the unity within them. They have a harmony that the other "books" do not have. And, I'm not talking about just the New Testament. The New Testament is in harmony with the old. The old with the new. They tell one story from the beginning of time until now of One God and His message to mankind. No other group of writings (be they the pseudo this and that or even the apocrypha) comes close.
So, frankly it wasn't the Church's judgment I trusted in to get the Canon right. It was the Holy Spirit's guidance. He can make an ass speak. He can certainly make a group of people from disparate backgrounds do what He wills them to do.
Regarding the church's judgment, I will take Paul's que here.
ACTS 17
10And the brethren immediately sent away Paul and Silas by night unto Berea: who coming thither went into the synagogue of the Jews.
11These were more noble than those in Thessalonica, in that they received the word with all readiness of mind, and searched the scriptures daily, whether those things were so.
The "Church" isn't wrong on everything. But what they make pronouncements upon MUST stand up to the Scripture test. If it contradicts Scripture, it should be tossed. That is the standard. Subjective? At times. But not so much as you "non-sola-scriptura types" would imagine. There is one Spirit. He leads me in the right path.