Thanks for feedback guys. Since people already implement RFC6979, lets use it.

Question: why HMAC-SHA512 is preferable to HMAC-SHA256? Only to be the same as in BIP32? But unlike BIP32, here we do not use extra 32 bytes output and would simply throw it away. Is it correct that SHA512 is faster than SHA256 on 64-bit systems, so using HMAC-SHA512 would allow better singing performance?