The doctrine of sola scriptura makes no claim against traditions or teachings that do not directly conflict with the Scriptures themselves. Not sure what is so hard to understand about that. You're beating up a strawman of your own creation.
To put it as plainly as possible, when serious Protestants talk about sola scriptura, we're essentially saying that we use the Bible as a sort of measuring stick against which to judge all other teachings, traditions, philosophies and world views. We do this because the Bible was written under the direct inspiration of the Holy Spirit (and is thus the literal word of God) and is an unchanging standard (like God himself) that perseveres through time. Thus, if any teaching (whether from the world or from other Christians) runs directly counter to what can be plainly read and understood in scripture, then we reject it out of hand. It's really that simple.
The objections you raise about the early church not having compiled the totality of the Biblical canon are irrelevant and somewhat nonsensical. Clearly things were different in the Old Testament era and in the days of the early Church (especially prior to the printing press and the widespread availability of the Bible). But God was always working toward a plan - just like He was always working toward a plan to redeem humanity through the person of Christ himself. And God had a plan for the early church, just as he had a plan for the church in the Middle Ages and up through the modern era. God has always and will always provide a path for his faithful elect. And a large part of that plan over the past several hundred years has been in the widespread availability of the Bible, which has helped to spread the Gospel to literally every corner of the world, as Christ commissioned us to do.
Rejecting sola scriptura on the basis that it couldn't have logically applied in the days of the early church is sort of like rejecting the idea that fully grown man will have much different needs and behaviors than a newborn child. A newborn baby is weak and vulnerable, and special allowance must be made for its survival - just as God made special allowance for the early church to grow and thrive by divinely empowering the Apostles and inspiring the writers of the New Testament. Those days of the early church were foundational, the roots on which the faith would grow. And the writing, safekeeping and eventual widespread distribution of the New Testament represented the ultimate blossoming of the faith. But roots and flowers alike are of the same plant - one plant - just like we are all ultimately of the one body of Christ. And because this is clearly how things have unfolded through history, we can only assume that this was part of God's grand design, and all for His ultimate glory.