Distilling large reasoning models (LRMs) has become essential for making their Long-CoT reasoning capabilities practical, as full-scale inference remains computationally prohibitive. Existing curation-based approaches, which select complete reasoning traces post-hoc, overlook the collaborative potential of heterogeneous teachers and fail to adapt exploration dynamically, often leading to redundant sampling and missed opportunities for complementary reasoning. To address this, we introduce CoRD, a collaborative multi-teacher decoding framework that performs step-wise reasoning synthesis guided by predictive perplexity–based scoring and beam search. This approach enables heterogeneous LRMs to jointly construct coherent reasoning trajectories while maintaining diverse, high-potential hypotheses efficiently. Experiments show that CoRD generates higher-quality reasoning data and achieves student performance approaching teacher-level results, demonstrating that fine-grained collaboration among diverse LRMs yields structured, efficient, and robust reasoning distillation. The dataset and model are available at https://github.com/DISL-Lab/CoRD