Document-level Event Causality Identification (DECI) aims to identify causal relations among multiple events within unstructured text. Existing methods predominantly rely on local semantic similarity for independent event-pair discrimination, thereby overlooking the influence of the overall narrative backbone in the propagation of causal dependencies and the role differentiation of events within multi-cause/multi-effect structures. Therefore, we propose a suggest-verify-revise approach for document-level Event Causality Identification with narrative consistency (SVRECI). In the suggest stage, we integrate multi-dimensional heuristic causal suggestions generated by an LLM with structural suggestions derived from hypergraph modeling to provide multi-source initial support for candidate event pairs. In the verify stage, we introduce a Topological Hawkes process to perform constrained verification of narrative propagation consistency among events. In the revise stage, we construct a dynamically evolving document-level causal graph and incorporate a structure-aware dual-level contrastive learning mechanism at both the event and event-pair levels, iteratively reducing noisy edges over multiple iterations. Experimental results on EventStoryLine and Causal-TimeBank datasets demonstrate that our approach outperforms previous methods.