What if you break the company in two companies (or more) ? The problem may be trying to keep a flat looking small pyramid look small, when it is in fact starting to show its real face.

I don't know if it's even possible, but why not push a small group to become owners of their own shop, outsourcing work to them ? This might push those small groups to seek other connections to the external world and thus build strength and resiliency.

Of course this implies giving up the money. This is probably where the core tension lies. I guess many wouldn't even want to think about it.