God worked through Herod and Pilate indeed. Here's what God didn't do. He didn't use them to preserve His Scripture. It is a case of apples and oranges, and it won't change the fact that the Bible is a Catholic book. Nor does it change the fact, that the Catholics who chose it actively believed it supported their doctrines.
Your quote from II Timothy is good, but it fails on a couple of points. First, while it may not mention "church," neither does it mention "only." Why should I assume that Scripture is the only thing that serves that purpose? That passage does not give any reason to think that.
How about if a mother said something like this: "Spinach is given to us by God, it is good for nutrition, discipline, and making you strong in life." Spinach is good for discipline; I can't stand the stuff. If a parent actually fed her child only spinach, she needs to be arrested. It would kill the child.
Now, the second it falls short on, is v14. Paul tells them to "continue in what they have learned and have become convinced of," putting Timothy's beliefs before he mentions Scripture. Why? "Because you know those from whom you learned it." Now, since Paul has established a community...he moves on to Scripture, and all the things it is good for.
The third thing you forget, is that the Scripture Paul is referring to here must be the Old Testament, maybe with some pseudapigraphic books. It doesn't include the New Testament. So, if you assume this teaches that Scripture alone is sufficient, then throw out your New Testament to be consistent.
All together, then, I do not see anything in II Timothy 3.15-17 that teaches Sola Scriptura. In fact, with those three points, I can use the passage to teach against it. Of course, since you believe that the Catholic Church chose and preserved the Bible accurately, despite believing it contradicts it, and since you believe that II Timothy plainly teaches this, I have one request. Will you show me one person in the first thousand years of Christianity who interpreted it as "Sola Scriptura?" If it clearly teaches that, then somebody will have interpreted it that way.
You are right in II Peter 1.20-21...partially. Peter opens for our topic in 1.16. He explains the importance of Scripture, and its inspiration. Naturally this culminates in 1.20-21. Next he proceeds to false teachers and false doctrines. In vv 2.3 we read that they deceive the people, "By covetousness they will exploit you with deceptive words: for a long time their judgement has not been idle, and their destruction does not slumber."
Now, with this, we can look back at v. 21. We both know that Greek isn't English and operates differently. Now, it says: "touto proton ginoskontes oti pasa prophitia graphis idias epilyseos ou ginetai." "Ginetai" is a linking verb that can also denote "appear," "came to be," "to be born." Now, "of one's own interpretation" and "from the prophet's own interpretation" are both translations of the genitive. The genitive can be used as a form of origin like the "from" or it can be used as a source of instrumentality like "of." This means that both translations are valid. It is quite possible that both senses were intended.
If we are to choose one, then we must choose "of," though. The purpose of II Peter wasn't to exalt Scripture. The passage on Scripture was an affirmation of its importance, as a preface to the blasphemy of false teachers twisting it. The verse in question is placed in the transition from affirming Scripture to rebuking false teachers. As "of" it fits that transition nicely. As "from," the transition is rather sudden.
Another thing that speaks against a sole use of "from" is that "prophitis" never appears, but only "prophiteia." Thus, the addition of "prophet's" is a gloss in the translation. I'm not saying that is bad. I will say that it was probably doctrinally motivated, because it isn't necessary.
Now, Peter closes with the rebuke on those who twist Scripture according to their own doctrines (3.16). This fits nicely with "of" also. They also fit the situation in the first and second centuries, as one sect after another broke off and started teaching rather ridiculous things.
So, if you don't feel that this rebukes Sola Scriptura, then please offer a counter-interpretation as I have done. As it stands, I stand by my statement that taking the Bible as sufficient in itself for faith is contrascriptural, and that there is no supporting evidence for it in Scripture.
