Whether there is proof or not depends a great deal upon STANDARDS of proof. I think that Catholics and Protestants do not have shared standards of proof, they do not share standards as to what counts as a scriptural proof. Even Protestants have various and diverging standards as to what counts as "proving" something from Scripture. But this raises many more problems for the "sola scriptura" people than it does for Catholics. And what counts as a "conclusive" argument? Usually, by "conclusive" people mean: it is impossible for it to be the case that A if evidence E is proposed" But that is an extremely high standard to apply. Is that what you mean?
Furthermore, I urge you to read some of the philosophers of science, such as Polanyi and Kuhn, who have made compelling arguments that in the sciences the capacity to follow proof or to grasp evidence is a function of having apprenticed oneself to an expert in a tradition of enquiry in which certain perceptual skills, habits of investigation, patterns of thought, vocabulary, and fundamental presuppositions are cultivated and imbibed. This is why non-experts in the sciences cannot follow the proofs the experts propose to each other. The same holds in scripture studies. Only those who are willing to apprentice themselves to an expert practitoner in a tradition of scriptural exegesis have the capacity to follow the proofs that are drawn up. The insight into the proofs is a good internal to the practices of the tradition of enquiry. These converts see the Church's proofs because they are converting, that is, they are abandoning a whole set of perceptual skills, habits of investigation, patterns of thought, vocabulary, and fundamental presuppositions, and they abandon it in favor of a catholic way of approaching the text, and they do so as motivated by deep and systemic failures in the Protestant approach to Scripture.
One of those failures is the naivete involved in the Protestant tradition. The Protestant tradition is one which requires its practitoner to hold "tradition is a bad thing, it interferes with thought, get back to the purity of the text without the mediation of human tradition" and then the practitioners of Protestant exegesis have gone on to develop a whole human tradition of exegesis, a tradition in which Protestant seminarians and theology students are apprenticed into for many years, and a tradition in which certain patterns of thought, perceptual skills, habits of investigation, etc, are cultivated and imbibed... It is all really rather self-contradictory it seems to me. Everyone has a tradition, just by virtue of being human. God knows this, so he set up a tradition for us, and by the ways of reading the texts internal to the sacred tradition of the Catholic Church, the proofs of the Marian dogmas are quite compelling indeed. What is lacking is not proof, but the capacity for following proof. Only tradition is a force for cultivating such a capacity.
St. Augustine discovered the same thing. In the Confessions he relates how he had for many years difficulites in dealing with Scripture. It seemed to him self-contradictory, obscure, and rather dry in comparison with Cicero. Only when he met Ambrose, and sat at the knee of Ambrose for some years, did he learn the right way of approaching Scriputre so as not to handle it in an intellectually clumsy way.
I'm a fair-minded guy, imho, and I'm not convinced that those arguments are any better than those on the other side. And they are not proof. (Locked and shut case.) As far as being an apprentice...I said I was a pastor. I've been at this a number of years. I wouldn't call me an apprentice. Now, answer me this: would you rather have a written Constitution of the United States of America? Or would you rather have a Congress that had not written document but could govern merely by majority rule? Or a president who could govern by consensus of counselors?
As a late comer here, and reading both your exchanges, I'd like to add an important point from the Catholic point of view to the above:
The proof comes from the Divine Grace of God working through Divine Faith. Otherwise there would be no reason for Divine "Faith".
Take this line from your (xzins) Post 70:
Where would you place "the full inspiration of scripture by God?" I would give it a 10.
I would give it a 10 too, except the proof comes from the Grace of God working through Faith in me. From the Holy Scriptures themselves, read by an individual separated from the Church, it's not possible to consider giving it a 10. The Scriptures themselves, particularly the New Testament, don't give me the information on just what Books are supposed to be there and which are not. It is the living, Divinely instituted Church, led by the Holy Spirit which authoritatively, the Authority of Christ no less, can tell me and others which Books are the Canon of Holy Scripture.
A non-Christian not open to Faith would just consider your "proofs" of the Bible being the Word of God as being "rationalizations".