A note about combining SHA512 with bcrypt: Don't feed the raw binary output of SHA512 into bcrypt. Use the hexadecimal or base64-encoded form instead. (Dropbox probably does this already, since they mention base64 in passing.)
bcrypt is known to choke on null bytes. Each SHA512 hash has a 25% chance of containing a null byte if you use the raw binary format.
Using hex or base64, of course, decreases the amount of entropy that you can fit into bcrypt's 72-byte limit. But you can still fit 288 to 432 bits of entropy in that space, which is more than enough for the foreseeable future.