As regards teaching the avoiding technique and the steep turn et all... when I learnt to fly I remember having a good 30 mins flying time with my instructor calling out "avoiding action - contact left/right - avoid" on a couple of trips just so that I could explore the envelope of the aircraft and be ready for any situation. The aircraft was a PA38 so uncontrolled roll was a certainty!
Anyway as an instructor, I teach avoiding action and yes it is not specifically in the syllabus but a competent instructor who knows of the dangers can easily work it into Ex15.