You could use Win32 API functions like CreateFile() etc. and wrap them into a class. These functions do not have the 2 GB problem and they are better behaved than Fox' low-level file functions anyway.

The classy approach also has the advantage that you can switch implementations from Fox LLFF to Win32 API file functions or memory-mapped files or whatever simply by instantiating different classes/implementations, without having to change any of the user code. Class methods and API calls do have a noticable call overhead compared to LLFF, though.