I see a few pathways:
In our organization we have coaches and mentors for specific things at the GCC level that all circles have access to call on when needed. (NVC, GTD, Holacracy)
Like you originally said, You could make an accountability for each subcircle to support Asana use within the circle. Then subcircles can do that how they see fit.
Or you could have an Asana Disciple at the GCC level and co-fill it with someone from each of the groups you think might benefit from support.
Another thing we do is draft governance then offer it to the groups so one classroom adopted a parent communication role and shared the success of the new role with their colleagues and within a month each classroom had developed some version of it not because they had to but when someone named that tension and solution they thought it would be helpful in their circle too.
Hope those pathways are helpful.