Undersampled magnetic resonance imaging (MRI) reconstruction seeks to recover temporally or contrast-varying image series from incomplete multicoil k-space data while preserving state-dependent fidelity for dynamic and quantitative MRI (qMRI). Existing scan-specific implicit neural representations (INRs) often use monolithic spatiotemporal coordinate fields, explicit subspaces, motion or deformation models, calibration variables, or sequence-specific quantitative signal models. These design choices can limit flexibility in sharing spatial information while adapting image synthesis across acquisition states. Moreover, many INR-based baselines remain computationally demanding, typically requiring per-scan optimization times on the order of hundreds to thousands of seconds. We propose MoE-dqINR, a scan-specific multicoil MRI reconstruction framework that factorizes the image-domain representation into shared spatial experts and a state-conditioned routing pathway. Spatial experts encode reusable coordinate-dependent image content, whereas routing weights, conditioned on ordered acquisition states, synthesize each dynamic frame or contrast state from a common expert bank. The representation is coupled to a multicoil MRI forward model, uses the normalized state index to drive routing in both dynamic and quantitative MRI. By separating shared spatial representation from state-dependent synthesis, the framework provides an image-first architecture for dynamic and quantitative MRI while reducing scan-specific INR optimization to approximately 30 s per scan in our experiments. The proposed formulation establishes state-conditioned mixture-of-experts INR as a scan-specific multicoil MRI reconstruction prior that unifies shared spatial representation, dynamic- and qMRI-specific synthesis, and practical per-scan efficiency.