The imminent threat of cryptographically relevant quantum computers to blockchain infrastructure presents a fundamental engineering challenge we term the PQC Blockchain Migration Trilemma: existing migration approaches cannot simultaneously achieve quantum security, performance parity, and backward compatibility with deployed infrastructure. This paper formally characterizes this trilemma, proves its existence through incompatibility analysis of current PQC standards including CRYSTALS-Dilithium, FALCON, and SPHINCS+, and proposes the Adaptive Quantum Migration Protocol, or AQMP a novel framework employing temporal decoupling, ZK-aggregated PQC proofs, dual-commit layers, and decentralized quantum threat oracles to resolve all three dimensions concurrently. Simulation results demonstrate AQMP achieves a 93% security score, 87% performance score, and 91% compatibility score the first proposal to break the trilemma. We analyze deployment pathways for Bitcoin, Ethereum, and permissioned blockchains with estimated migration timelines of 24 to 48 months with zero downtime.