1. Access to information in a need-to-know basis only using strong enforcement via MAC. Nobody has ALL the information on a specific subject.
2. All applications are used via virtual desktops accessed from secured, fully managed devices. No access is allowed from unmanaged endpoints of any kind.
3. If some information is as sensitive as described, then physical security enforcement need to be in place (isolated terminal room for example).
4. No printing, no emailing, no networking outside the proper security perimeter.
5. Regular audits and interviews to personnel with access to specific pieces of data.
You'll have to sacrifice convenience for security in environments that require that.
Gee, Toto, I don't think we're in Kansas anymore.