I know it's possible to prevent any USB sticks from being mounted, but is it possible to (somehow) only allow some USB sticks (either by volume name, a key file on the stick, or some other mechanism) while denying others?
Here is a possible solution, hinging on user permissions and drivers. Essentially, you remove all USB drivers for USB drives, and only allow certain drivers. That way, unless someone knows what kind of drive you use, they won't be able to use theirs. Lockdown USB to Specific Removable USB Drives
Edit: Here's another article that provides some powerful techniques for Windows 7 specifically. Locking down Windows Vista and Windows 7 against Malicious USB devices