Massive heterogeneous IoT networks encounter significant random access (RA) challenges due to diverse Quality of Service (QoS) requirements and resource constraints. To address these issues, we first propose a fuzzy logic-assisted multi-criterion access priority ranking (FL-MCAPR) scheme to prioritize RA for IoT devices, integrating delay, channel interference, and energy factors. The resulting suitability values enable adaptive and fine-grained backoff adjustments in large-scale IoT deployments. Next, hybrid RA control schemes with a deployability-descending double-queue (D3Q) structure and access priority-backoff window model optimize preamble and backoff allocation. In addition, preamble parallelization and early-stage collision detection enhance RA throughput by expanding resources and reducing collisions. Using D3Q, the analytical RA throughput is derived, informing an optimization problem to determine Access Class Barring (ACB) factors balancing low delay and energy efficiency, considering all RA resources. Building on these results, the hybrid fuzzy logic-guided RA management (HFL-RAM) scheme is developed for comprehensive RA management, systematically evaluated in terms of delay and throughput. Finally, a lightweight pseudo-Bayesian estimation method is applied, which relies solely on two observable quantities to estimate the contending MTCD traffic. Simulation results demonstrate that the proposed HFL-RAM scheme consistently outperforms conventional approaches, effectively managing traffic heterogeneity across a wide range of traffic loads.