Increasing Entropy of Limited Information / ID
I tried to figure out salting it, but since the main problem is the
  entropy is too small, i don't think it might work as expected.  


With your "salt" being a long, high-entropy and secret blob, it should work alright.  

But even more important, don't use a single SHA512. SHAs are fast, that's bad if you want to prevent bruteforcing. There's eg. PBKDF2 or bcrypt.