When defining a list style set, you need to start at level 1 and define for each level down to the level you want to change. I generally define all 9 levels because that is how I am.
I do not know that this is where you are running into problems, but it is the most frequent error people make.
What are you attaching to the QAT? How? Why are you not putting it in the Quick Styles Gallery?
Control the Quick Styles gallery on the Home Tab