I will agree with the assertion that 'what contradicts Scripture' must be tossed, however, with two provisos: first, provided the Scriptures are 'rightly divided', that is rightly interpreted, and second, that we accept the judgement of the Church, not the Christ-denying rabbis who met a Jamnia in 90 AD, as to what constitutes the Scriptures of the Old Covenant.
However, I have observed that most 'sola scriptura' types go a step further than what you have advocated, and toss not only what contradicts Scripture, but anything their discursive human reason cannot derive from Scripture. 'Sola scriptura' invariably disolves into private interpretation, with a hermeneutic that ignores the problem of intepretation, and rejects the context in which the Scriptures were written and canonized--the life of the Church--and insists that whatever the interpeter cannot *prove* from Scripture is false. This last is a much stronger assertion than you made, and is contrary to the plain word of Scripture, since a report of one of the deeds of Christ alluded to by the conclusion of the Gospel of John could not be proved from Scripture, but would not be false.
Christ promised His disciples that the Holy Spirit would lead them into all truth. It seems to me a very odd faith to believe that that leading into all truth is confined to the fixing of the canon of Scripture, and does not also extend to the Church judging the content of the Proto-Evangelium of James of the Didache, of accounts of the lives of the saints (as, for example The Martyrdom of Polycarp) to be sound and truthful, even though none of these documents meet the standard of undoubtable Apostolic authorship. (The Didache is a set of 'lecture notes' on the teachings of the Apostles, refered to in ancient patristic texts, a copy of which was found in the library of the Great Chruch of Constantinople in the 19th century.)
What truth is there outside the word?
I've read the Didache and am aware of many (not all) of the non-canonical books.
Also, I believe the clear teaching of Scripture is that the Holy Spirit guides ALL believers into the truth. This doesn't mean that everything believers or church bodies struggle with is the truth. The Corinthians, Galatians, Ephesians, Thessalonians, etc., certainly had issues that they struggled with. And many of the churches in Revelation seemed to officially sanction some really bad things (putting up with the doctrine of the Nicolaitans, and allowing the harlot 'Jezebel' to spread her heresies being examples).
So, with that said, just because it is more than one person, doesn't mean that it is inspired by the Holy Spirit. I believe many doctrines that have gotten the support of the church over the years fall into that category.
Other things that have come about, I do not see any contradiction with Scripture and while they may not be my experience; generally, I keep an open mind as to them occurring. For example, some stories I have heard of some really wild things happening to missionaries, including a few stories of raising the dead. It happened in Scripture. I never hear of it happening in these parts today. But could God do it? Yes. And so, I reserve judgment on it (unless the person claiming it is known to be a false prophet or something to that affect).
So. You are correct. I do not demand that everything be able to be proved by Scripture before I give it the possibility of being true. But I do demand that it not stand in opposition to Scripture.
Like the famous saying; in essentials unity, in non-essentials liberty, in all things charity.
The Holy Spirit is not for pontiffs and priests. He is for all believers. He indwells all believers. He is our comforter and our teacher. We don't always listen. We don't always get it right. And sometimes, we even fight amongst one another. But it makes it no less true that He is here.
Earlier on the thread, I mentioned how I believe that Christ left some things in scripture ambiguous so that we would struggle with one another over it. It is called Iron sharpening Iron. We believe something. It is contradicted by another person. And then we are left to dig in Scripture to see if we have the support needed to back up our belief. Some struggling and debate is good for us. And, yes, I believe that God designed it that way.
If we never argued over anything, what would cause us to dig in His Word?