Ability to privatize C360's for specific customers?

Due to some specific customer requirements, we have a need to make certain C360's only viewable to the AM and CSM assigned. Most important is to hide Timeline notes to only these users. Does anyone here know how I can solve this problem? I understand that C360 layouts doesn't allow for this, since all can still see the different layouts. Someone mentioned  salesforce record-level security as well. 

Appreciate the input. This is an important requirement for us.