As some background, my company is currently using an Apple Calendar server, some Exchange servers and a Google Apps subscription to provide calendaring for different parts of the organization. I've been tasked with providing free/busy access across these services while we try to take at least one of the services out of the equation.
I've attempted to use Google Interop, but it does not work with Exchange 2013 due to Microsoft eliminating Exchange Public Folder Databases in that release. I've also set up an IIS WebDAV server to attempt to share calendars, but this has shortcomings as well because only one person is able to moderate the calendar, and f/b data can't be queried in the Apple Calendar app - you have to subscribe to a separate f/b calendar.
Are there any suggestions as to how I should proceed?
If you can write your own connectors for each service (ie using propietary API's) you could then expose that information through a custom caldav service.
For example you could use http://milton.io (java) or http://sabre.io/ (php), both allow pulling data from arbitrary data sources.