I decided to give AMD a call to inform them of the issue and they immediately got in touch with Electronic Arts to try and work through the issues. AMD's official response to us was "Thanks for bringing this to our attention, we are now fully engaged with EA, and are helping them any way we can to patch the game for users experiencing crashes. Although the updates from the patch will have to come from EA, all I can say is that they have our full engineering support to root cause the issue."
AMD are now working with Electronic Arts to resolve these issues for AMD/ATI users. More details at DriverHeaven.