Spoken interaction is moving from alternating turns to full-duplex conversation, where an agent listens while speaking. Learning this coordination requires natural dialogue with persistent speaker-resolved tracks, a data requirement that remains difficult to satisfy at scale. Generative recovery offers a route from ordinary recordings, but recovering two voices is not enough: their track assignments can drift as the conversation unfolds. We address this missing link with speaker-anchored routing before diffusion: a 1.84M-parameter module matches the separator's coarse streams to fixed enrollment identities and orders them before a frozen generator reconstructs the speech, without retraining the generator or altering the reconstructed audio. On 25-minute remote conversations, routing cuts wrong-track time from 43.9% to 4.1%, below the 6.2% of matched-enrollment waveform re-identification, with its largest advantage when one participant holds the floor (17.8% versus 28.6%), and raises fixed-track activity F1 from 0.46 to 0.84 while per-chunk reconstruction quality is unchanged. The same router transfers to unseen face-to-face and telephone recordings, and a margin-gated verification step brings their wrong-track time to 0.9-1.7% while embedding 20-36% of the output, where full re-identification embeds all of it. Recovered voices thus become the participant-consistent tracks that full-duplex dialogue modeling needs. Audio examples: https://elpsykongloo.github.io/beyond-two-tracks/

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