What I am looking for is something I can show to the beginner white belts so they can use it while rolling against blue/purple belts. The closest thing in your list to that is "half guard basics". But then again, if they try getting underhook as you suggest they will just get an armbar on that far arm. What I typically see in BJJ is that beginners are taught how to attack before they taught how to defend (if they taught at all). They try attacking from unprepared positions and are becoming an easy target for the higher belts. One example that I show to beginners is "embryo defense". Elbows to the chest, knees around elbows, shoulders up, all rolled into a tight ball. Then I move them around from side to side, into turtle, back take to let them feel that they are secure as long as they stay in that position. Next I show them how they can open up to get advantage from the bottom position. E.g. how to create good base with legs and turn to the shoulder in side control while still staying safe. I set their goal in rolling as not getting tired and not getting tapped instead of trying to tap a purple belt. Once I show that to them I see tremendous difference in they rolling. They still do attack, but they no longer attack from bad positions. Once their attack fails they retreat and stay calm waiting for another opportunity and gaining position advantage inch by inch. These are things I am trying to find. Basic positioning, basic choke/armbar defense, breathing, etc.