Have you looked into ModX. Instead of a regular CMS (content management system), it is a CMF (content management framework). They call it “extensible by design”. There are two types, Evolution and for bigger sites Revolution. The best thing about it is that it puts all of the tools at your fingertips to write your own ticket, rather than having to make your needs fit into someone else’s plan.
We were looking for a similar tool about a year ago. We settled for something of our own eventually. I think it is well worth hiring a PHP programmer to whip up an application for you which can do everything you want it to do as against getting 3rd party apps to do what we want.