Restoring a large iCloud backup to a smaller iPhone...

How would you restore an iCloud backup from a larger capacity phone to a smaller 5C?

So my friend lost her iPhone, bought a 5C, and can't restore from backup because the backup file is too big -- her old iPhone had a larger capacity than the 5C she's replacing it with.

Apple is telling her there's nothing she can do to access that stuff, but I find that hard to believe.

Does anyone have any ideas? Either restoring all settings without content to save space would be cool, or just being able to access the Camera Roll backup from a Mac would also be sweet.

Thanks, all!