Robot swarms offer inherent robustness and the capacity to execute complex, collaborative tasks surpassing the capabilities of single-agent systems. Co-designing these systems is critical, as marginal improvements in individual performance or unit cost compound significantly at scale. However, under traditional frameworks, this scale renders co-design intractable due to exponentially large, non-intuitive design spaces. To address this, we propose SwarmCoDe, a novel Collaborative Co-Evolutionary Algorithm (CCEA) that utilizes dynamic speciation to automatically scale swarm heterogeneity to match task complexity. Inspired by biological signaling mechanisms for inter-species cooperation, the algorithm uses evolved genetic tags and a selectivity gene to facilitate the emergent identification of symbiotically beneficial partners without predefined species boundaries. Additionally, an evolved dominance gene dictates the relative swarm composition, decoupling the physical swarm size from the evolutionary population. We apply SwarmCoDe to simultaneously optimize task planning and hardware morphology under fabrication budgets, successfully evolving specialized swarms of up to 200 agents -- four times the size of the evolutionary population. This framework provides a scalable, computationally viable pathway for the holistic co-design of large-scale, heterogeneous robot swarms.