Funny little problem this one. Magento Enterprise 1.11 does not use the theme name as part of the FPC uri. Therefore when switching themes within a package using the design exceptions you still see the cached version of the site. This is obviously a major issue when you're using the design exceptions to load a mobile theme.

Solution

Pretty straightforward, add the theme name to the FPC uri. It doesn't need much explaining so grab the source on Github.