Can you express this with Noise framework tokens? I don't think you can. Noise is fiddlier than it looks! It's not just an ordering of DH exchanges; it's transcript hashes, cipher state tracking (and reinitializing), key derivation, the whole 9. The temptation (at least for me) is to just skip to the table of handshakes and skim, but the actual protocol framework is in Section 5, where they define precisely what each of those tokens really entails.
(To say nothing of: this uses signatures, and Noise does not).