The work on the new conduit is steadily progressing and will be integrated in a new major release of cohttp in the future, once we will be confident that the API is settled. If you want to try using it immediately, then it is available as the mimic library in ocaml-git.
I just take the opportunity to show up a tutorial about mimic which is now available into the distribution of it: see here. Thanks for your work about the release process.