2 Tim. does not exclude anything else, it excludes anything else EXTRA. So, if I taught orally, right from the Bible, that would be good. Sola Scriptura does not mean that the only way to get good information is to read it directly by yourself. Teaching from the Bible is good. Speaking of this, your Ephesians passage means what I just said in this context, that teaching is good. It certainly does not imply to teach outside of what is now the Bible.
If you believe that MORE is needed, besides scripture, then you must believe that "thoroughly equipped" is not good enough. What can Tradition add to "thoroughly equipped"?
It does not such thing. It says that Bishop Timothy will be fully equipped for his work if he supplements his formation with the study of the scripture. But Paul says so only after he exhorted him to heed the lessons St. Paul and apparently others gave him orally (2 Tim 3:14). Likewise, the Catholic Church teaches that one can profit from reading the scriptures if such reading is combined with solid catechism.