"[Timothy per 2 Timothy 3] is only supplementing the OT with what he is now learning as what would become the NT"
This is the Evangelical Free Church Statement of Faith concerning the Scriptures. It encapsulates Paul's thinking on the efficacy and authority of the scriptures
2. Gods gospel is authoritatively announced in the Scriptures
We believe that God has spoken through the Scriptures, both the Old and New Testaments. They are the verbally inspired Word of God, without error in the original writings, the complete revelation of His will for salvation, and the ultimate authority that stands over every realm of human knowledge and endeavor. Therefore, the Bible is to be believed in all that it affirms, obeyed in all that it requires, and trusted in all that it promises.
Of course. I could sign it. But this is not what Sola Scriptura is, as your statement does not exclude apostolic guidance received from the Church and not contradicted by the scripture.
Now, perhaps if they practiced what they preached, we'd be all one big, happy family. For in those same Scriputres, it tells us such things as "faith alone is dead" and "Hold onto the traditions given to you, whether by word or written letter". Somehow, those "Words of God" are ignored...
Regards