I use dovecot as my mail transfer agent and I aim to use the strongest password scheme which is supported by my system: SHA512-CRYPT or SHA256-CRYPT (BLF-CRYPT doesn't work).
For my own written webinterface I look for a function or library in node.js for hashing a password (with SHA***-CRYPT).
You may consider checking: https://github.com/mvo5/sha512crypt-node which contains a implementation for sha512crypt in JS. Its very new but passes the testvectors from the glibc reference implementation.
Have you seen this page: cryto.createHash sha512 with hexDigest input type
You can use crypto.createHash function, but why SHA512? Are you sure you need it for your website?