Is it OK to use r-value from ECDSA signature (r, s) to prevent replay attack?
I have to be honest and say that I never really understood why systems use the signature as the record rather than just the hash of the message that was signed. If that was used, then there would be no problem with using malleable signatures. If someone has a reason why not to just do what I said, please let me know and I'll change the answer.
More to the point of the question, there is no reason why not to just use the $r$ portion. If this repeats in two different valid signatures, then the signers can each learn the other party's private key. This is because by dividing the $s$ portions in the signatures, the $k^{-1}$ part falls away. Then, given one of the private keys it is easy to learn the other private key. As such, this should not be a concern to anyone (i.e., if it could happen then malleability is far from the problem).